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Vector Dot Product

Vector Dot Product

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cause-effect pairs


 »  Two vectors that are cause-effect pair will be in same direction
    →  `vec x` is the cause
    →  `vec y` is the effect of the cause
    →  both `vec x` and `vec y` will be in same direction


 »  Dot product is defined for applications with product involving cause-effect pair

 »  Note: the dot product is used in applications where parallel components take part in multiplication

Cause-Effect Pair

plain and simple summary

nub

plain and simple summary

nub

dummy

Two vector quantities may be in relation as cause-effect pair.

The result, due to a cause, will only be in the direction of the cause.

simple steps to build the foundation

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simple steps to build the foundation

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In this page, the primary application of vector dot product "cause-effect pairs" is explained.


Keep tapping on the content to continue learning.
Starting on learning "Cause-Effect Pair". ;; In this page, the primary application of vector dot product "cause-effect pairs" is explained.

In this chapter, the product defined for components in parallel is discussed. First, let us establish the application scenario where components in parallel interact to form a product.

A pen can be used to write `30` pages. How many pages one can write with `4` pens?

  • `4xx30`
  • `120`
  • both the above

Answer is 'both the above'. In this 'number of pen' is a cause and 'writing a number of pages' is an effect.

This is an example of cause and effect pair in scalar quantities.

Can you identify a cause-effect pair in the following?

  • Volume of Paint and painted area
  • Number of tickets sold and the money collected in the sale
  • speed of a car and distance covered in an hour
  • all the above

The answer is 'all the above'.

Similar to the cause-effect pairs of scalar quantities, vectors have cause and effect pairs.

Can you identify the cause-effect pair in vector quantities?

  • pull a table and the table moves
  • electronic item heats up when they are used
  • click a photo using a mobile
  • none of the above

Answer is 'pull a table and the table moves'. Pulling force has direction and the movement of the table has direction. So, Both of them are vector quantities.

Can you identify a cause-effect pair in vector quantities?

  • velocity causes displacement
  • acceleration causes velocity
  • force causes acceleration
  • all the above

The answer is 'all the above'.

One pulls a table towards east direction, to which direction will the table move? (Given that no other force is acting on the table.)

  • towards east
  • towards west
  • towards north
  • towards north-east

Answer is 'towards east'.

One pulls a table in a direction. Is it possible that the table move in any direction other than the direction of force? (given that no other force is acting on the table.)

  • Not Possible
  • it is Possible

Answer is 'Not possible'.

If the force is in one direction, then the displacement due to that force is in the same direction.

A ball moves with velocity `vec v`. In which direction will the displacement due to that velocity be?

  • in the same direction as `vec v`
  • in perpendicular to `vec v`
  • in any direction
  • none of the above

Answer is 'in the same direction as `vec v`'.

A ball moves with velocity `vec v_1` in one direction and velocity `vec v_2` in another direction. In which direction will the displacement `vec s_1` due to `vec v_1` be?

  • in the direction of `vec v_1`
  • in the direction of `vec v_2`
  • in the direction of `vec v_1 + vec v_2`
  • none of the above

Answer is 'in the direction of `vec v_1`'.

A ball moves with velocity `vec v_1` in one direction and velocity `vec v_2` in another direction. In which direction will the displacement `vec s_2` due to `vec v_2` will be?

  • in the direction of `vec v_1`
  • in the direction of `vec v_2`
  • in the direction of `vec v_1 + vec v_2`
  • none of the above

Answer is 'in the direction of `vec v_2`'.

A ball moves with velocity `vec v_1` in one direction and velocity `vec v_2` in another direction. The sum of velocities `vec v = vec v_1 + vec v_2`. In which direction will the displacement `vec s` due to `vec v` be?

  • in the direction of `vec v_1`
  • in the direction of `vec v_2`
  • in the direction of `vec v_1 + vec v_2`
  • none of the above

Answer is 'in the direction of `vec v_1 + vec v_2`'.

Note that the displacement component is in the same direction as the velocity component causing it.
 •  `vec s_1` is in the direction of `vec v_1`
 •  `vec s_2` is in the direction of `vec v_2`
 •  `vec s_1+vec s_2` is in the direction of `vec v_1+vec v_2`

One pulls a table towards east and at the same time, another pulls the same table towards north. If both are pulling with same magnitude, what direction will the table move?

  • North
  • East
  • North-East
  • South-West

Answer is 'North-East'
This can be verified with a simple experiment at home / class.

The problem is shown in the figure.vectors direction being same The forces `vec f_1` and `vec f_2`. The combined `vec f_r` is shown. `vec f_r = vec f_1+vec f_2`. Which law of vector addition is used in this?

  • Parallelogram law of Vector Addition
  • Triangular law of Vector Addition
  • Both the above can be used interchangeably

Answer is 'Both the above can be used interchangeably'. Triangular law or Parallelogram law are to understand different aspects of vector addition, and both equivalently describe vector addition.

The displacement `vec s`, due to force `vec f`, is shown in the figure.vector force causing displacement Which of the following is understood from the figure?

  • `vec f_1` causes `vec s_1` in the same direction
  • `vec f_2` causes `vec s_2` in the same direction
  • `vec f_r` causes `vec s_r` in the same direction
  • all the above

Answer is 'All the above'.

If force `vec f` causes `vec s` displacement, then the work done by the force is calculated as
work = `f` multiplied by `s`

Given the force, displacement pairs in the figure, What is the work done by force `vec f_r`?vector dot product illustration

  • `f_r` multiplied by `s_r`
  • `f_r` multiplied by `s_1`
  • `f_r` multiplied by `s_2`

Answer is '`f_r` multiplied by `s_r`'. Because `f_r` causes `s_r`.

Given the force, displacement pairs in the figure, What is the work done by force `vec f_1`?vector dot product illustration

  • `f_1` multiplied by `s_r`
  • `f_1` multiplied by `s_1`
  • `f_1` multiplied by `s_2`

Answer is '`f_1` multiplied by `s_1`'. Because `f_1` causes `s_1`.

The force and displacement pair are given as in the figure. Note that only force `vec f_1` and displacement `s_r` are given. It is understood that some unknown force is also acting on the object. That is the reason the displacement is not in the same direction as the force.vector dot product illustration What is the work done by force `vec f_1`?

  • magnitudes of `f_1` and `s_r` multiplied
  • cannot compute using only the magnitudes

Answer is 'Cannot compute using only the magnitudes'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Direction Property of Cause-Effect pairs : When a vector quantity `vec x` results in another vector quantity `vec y` , the direction of the result `vec y` will be same as that of the cause `vec x`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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Progress

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Progress

In this chapter, the product defined for components in parallel is discussed. First, let us establish the application scenario where components in parallel interact to form a product.
A pen can be used to write 30 pages. How many pages one can write with 4 pens?
4;times;30
4 times 30
120;20
120
both;above
both the above
The answer is "both the above". In this number of pen is a cause and writing a number of pages is an effect. This is an example of cause and effect pair in scalar quantities.
Can you identify a cause-effect pair in the following?
volume;paint;area
Volume of Paint and painted area
tickets;sold;money;collected
Number of tickets sold and the money collected in the sale
speed;car;distance;covered
speed of a car and distance covered in an hour
all;above
all the above
The answer is "all the above". Similar to the cause-effect pairs of scalar quantities, vectors have cause and effect pairs.
Can you identify the cause-effect pair in vector quantities?
pull;table;moves
pull a table and the table moves
electronic;item;heats;up
electronic item heats up when they are used
click;photo;using;mobile
click a photo using a mobile
none;above
none of the above
Answer is 'pull a table and the table moves'. Pulling force has direction and the movement of the table has direction. So, Both of them are vector quantities.
Can you identify a cause-effect pair in vector quantities?
velocity causes;causes displacement
velocity causes displacement
acceleration causes;causes velocity
acceleration causes velocity
force causes;causes acceleration
force causes acceleration
all;above
all the above
The answer is "all the above".
Two vector quantities may be in relation as cause-effect pair.
One pulls a table towards east direction, to which direction will the table move? (Given that no other force is acting on the table.)
east
towards east
west
towards west
north
towards north
north-east
towards north-east
The answer is "towards east".
One pulls a table in a direction. Is it possible that the table move in any direction other than the direction of force? (given that no other force is acting on the table.)
not
Not Possible
it;is
it is Possible
The answer is "not possible". If the force is in one direction, then the displacement due to that force is in the same direction.
A ball moves with velocity v. In which direction will the displacement due to that velocity be?
same;direction;as
in the same direction as velocity v
perpendicular
in perpendicular to velocity v
any;direction
in any direction
none;above
none of the above
The answer is "in the same direction as velocity v"
A ball moves with velocity v 1 in one direction and velocity v 2 in another direction. In which direction will the displacement s 1 due to v 1 be?
1
2
3
4
The answer is "in the direction of v 1".
A ball moves with velocity v1 in one direction and velocity v2 in another direction. In which direction will the displacement s 2 due to v 2 be?
1
2
3
4
The answer is "in the direction of v2".
A ball moves with velocity v1 in one direction and velocity v2 in another direction. The sum of velocities v = v 1 + v 2. In which direction will the displacement s due to velocity v be?
1
2
3
4
The answer is "in the direction of v 1 + v 2 ".
Note that the displacement component is in the same direction as the velocity component causing it. ;; s1 is in the direction of v 1 ;; s2 is in the direction of v2 ;; s 1 + s 2 is in the direction of v 1 + v 2.
The result, due to a cause, will only be in the direction of the cause.
Direction property of cause-effect pairs: When a vector quantity x results in another vector quantity y, the direction of the result y will be same as that of the cause vector x.
One pulls a table towards east and at the same time, another pulls the same table towards north. If both are pulling with same magnitude, what direction will the table move?
1
2
3
4
The answer is "north east". This can be verified with a simple experiment at home or class.
The problem is shown in the figure. The forces f 1 and f 2 . The combined force f r is shown. Vector f r = vector f 1 + vector f 2. Which property of vector addition is used in this?
parallelogram
Parallelogram law of Vector Addition
triangular
Triangular law of Vector Addition
both;above;can;used
Both the above can be used interchangeably
Answer is 'Both the above can be used interchangeably'. Triangular law or Parallelogram law are to understand different aspects of vector addition, and both equivalently describe vector addition.
The displacement s, due to force f, is shown in the figure. Which of the following is understood from the figure?
1
vector f 1 causes vector s 1 in the same direction
2
vector f 2 causes vector s 2 in the same direction
r;are;or
vector f r causes vector s r in the same direction
all;above
all the above
Answer is 'All the above'.
If force f causes s displacement, then the work done by the force is calculated as ; work = f multiplied by s.
Given the force, displacement pairs in the figure, What is the work done by force f r ?
1
2
3
The answer is "f r multiplied by s r". Because f r causes s r.
Given the force, displacement pairs in the figure, What is the work done by force f 1?
1
2
3
The answer is "f 1 multiplied by s 1". Because f 1 causes s 1.
The force and displacement pair are given as in the figure. Note that only force f 1 and displacement s r are given. It is understood that some unknown force is also acting on the object. That is the reason the displacement is not int he same direction as the force. What is the work done by force f 1?
of;f;s;yes;multiplied
magnitudes of f 1 and s r multiplied
cannot;compute;using;only
cannot compute using only the magnitudes
The answer is ""

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