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summary of this topic

Vector Addition

Vector Addition

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Vector Addition : Parallelogram Law


 »  continuous addition of `vec x` and `vec y`
    →  `vec x = vec a + vec b`

    →  `vec y = vec p + vec q`

    →  the co-initial diagonal of the parallelogram formed by sides `vec x` and `vec y`

Parallelogram Law

plain and simple summary

nub

plain and simple summary

nub

dummy

Two vectors form a parallelogram and the co-initial diagonal is the sum.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, the parallelogram law of vector addition is explained as a continuous addition of vectors.


Keep tapping on the content to continue learning.
Starting on learning "Parallelogram Law of vector addition". ;; In this page, the parallelogram law of vector addition is explained as a continuous addition of vectors.

Note: Using Geometry, the triangle property of vector addition can be extended to explain parallelogram property of vector addition. In the coming pages, we establish a different point of view for the same.

Two taps simultaneously fill a bucket. One fills at `20` liter per hour and another fills at `10` liter per hour. What type of addition is this?

  • Sequential addition
  • Continuous addition

Answer is 'continuous addition'. It is called continuous addition as the quantities are added continuously in small quantities over time. Scalar quantities can be added continuously..

A ball rolls with two velocity components `2`m/sec at `11^@`angle and `1.3`m/sec at `67^@` angle. vector addition parallelogram law The effective velocity of the ball is calculated using...

  • Sequential addition of vectors
  • Continuous addition of vectors
  • This does not look to be vector addition

answer is 'Continuous addition of vectors' The two vectors are acting together resulting in a vector sum.

A table is pulled by two persons with forces `f_a` and `f_b` with an angle `theta` between the two forces. vector addition example parallelogram The effective force on the table is calculated using ....

  • Sequential addition of vectors
  • Continuous addition of vectors
  • This does not look to be vector addition

answer is 'Continuous addition of vectors' The two vectors are acting together resulting in a vector sum.

Continuous addition of two vectors is shown in the figure.
The magnitude of a vector is equivalently shown as length of the ray in a coordinate plane.parallelogram law of vector addition Let us see how to calculate `vec r`.

The vectors `vec x` and `vec y` can be split into components
 •  `vec x` = `vec a` + `vec b`
 •  `vec y` = `vec p` + `vec q`

parallelogram law of vector addition Note that `vec b` = `-vec q`
and `vec a` and `vec p` are in the same direction.

The component vectors are equivalently rearranged as shown in the figure.vector addition parallelogram law How will `vec a` and `vec p` interact?

  • Add in magnitude
  • Subtract in magnitude
  • cannot calculate

Answer is 'add in magnitude', as they are in the same direction

The component vectors are equivalently rearranged as shown in the figure.vector addition parallelogram law How will `vec b` and `vec q` interact?

  • cancel out to `0`
  • subtract in magnitude
  • both the above

Answer is 'both the above', as they are in the opposite direction.

Note that the result forms a diagonal to the parallelogram.vector addition parallelogram law This is given as the parallelogram property of vector addition.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Parallelogram Property of vector addition parallelogram law of vector addition when two vectors are added, arrange such that their initial points coincide. In that configuration, complete a parallelogram with the two vectors as the two adjacent sides. The diagonal that starts from the initial point of the vectors is the sum of the two vectors.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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Note: Using Geometry, the triangle property of vector addition can be extended to explain parallelogram property of vector addition. In the coming pages, we establish a different point of view for the same.
Two taps simultaneously fill a bucket. One fills at 20 liter per hour and another fills at 10 liter per hour. What type of addition is this?
sequential
Sequential addition
continuous
Continuous addition
The answer is "continuous addition". It is called continuous addition as the quantities are added continuously in small quantities over time. Scalar quantities can be added continuously.
A ball rolls with two velocity components 2 meter per sec in 11 degree angle and 1 point 3 meter per sec at 67 degree angle. The effective velocity of the ball is calculated using...
sequential
Sequential addition of vectors
continuous
Continuous addition of vectors
does;not;look
This does not look to be vector addition
The answer is "Continuous addition of vector". The two vectors are acting together resulting in a vector sum.
A table is pulled by two persons with forces f a and f b with an angle theta between the two forces. The effective force on the table is calculated using ...
sequential
Sequential addition of vectors
continuous
Continuous addition of vectors
does;not;look
This does not look to be vector addition
The answer is "Continuous addition of vectors". The two vectors are acting together resulting in a vector sum.
Continuous addition of two vectors is shown in the figure. The magnitude of a vector is equivalently shown as length of the ray in a coordinate plane. ;; Let us see how to calculate vector r.
The vector x and vector y can be split into components ;; vector x = vector a + vector b ;; vector y = vector p + vector q ;; Note that vector b = minus vector q ;; and vector a and vector p are in the same direction.
The component vectors are equivalently rearranged as shown in the figure. ;; How will vector a and vector p interact?
add
Add in magnitude
subtract
Subtract in magnitude
cannot;not;calculate
cannot calculate
Answer is 'add in magnitude', as they are in the same direction
The component vectors are equivalently rearranged as shown in the figure. How will vec b and vec q interact?
cancel;out
cancel out to 0
subtract;magnitude
subtract in magnitude
both;above
both the above
Answer is 'both the above', as they are in the opposite direction.
Note that the result forms a diagonal to the parallelogram. ;; This is given as the parallelogram property of vector addition.
Two vectors form a parallelogram and the co-initial diagonal is the sum
Parallelogram Property of vector addition: when two vectors are added, arrange such that their initial points coincide. In that configuration, complete a parallelogram with the two vectors as the two adjacent sides. The diagonal that starts from the initial point of the vectors is the sum of the two vectors.

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