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exercise provides practice problems to become fluent in the concepts.

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summary of this topic

Properties of Vector Multiplication by Scalar

Properties of Vector Multiplication by Scalar

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 »  unit vector along the direction of vector is the vector divided by the magnitude
    →  `hat p = (vec p)/(|vec p|)`

Unit Vector along a vector

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Unit vector in the direction of a vector is the vector divided by its magnitude.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, learn how to compute unit vector along a vector.


Keep tapping on the content to continue learning.
Starting on learning "Unit Vector along a vector". ;; In this page, learn how to compute unit vector along a vector.

Given the magnitude of a vector `|vec p| = 20` what is the magnitude of `(vec p)/5`?

  • `20`
  • `5`
  • `4`
  • `1/4`

The answer is '4'. It is `(|vec p|)/(|5|)`.

Given the magnitude of a vector `|vec p|` what is the magnitude of `(vec p)/(|vec p|)`?

  • 1
  • `|vec p|`
  • `-1`
  • `-|vec p|`

The answer is '1'.

Given two vectors `vec p` and `vec q`, how can you verify if the vectors are in same direction?

  • directional cosines should be equal
  • components along axes should be equal

The answer is 'Directional Cosines should be equal' along the respective axes.

Given two vectors `vec p` and `(vec p)/2`, are these in the same direction?

  • Different directions
  • Opposite directions
  • Same direction

The answer is 'Same Direction'. Direction cosine of `(vec p)/2` is same as that of`vec p`. Please verify this by working out.

It is shown that
 •  magnitude of `(vec p)/(|vec p|)` is `1`
 •  direction of `(vec p)/(|vec p|)` is same as that of `vec p`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Unit Vector along a Vector: The unit vector along a given vector `vec p` is given by
`hat p = (vec p)/(|p|)`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Find the unit vector along the direction of vector `vec p = 2i+2j+2k`

  • `1/sqrt(3) (i+j+k)`
  • `i+j+k`
  • `2/sqrt(3) (i+j+k)`

The answer is '`1/sqrt(3) (i+j+k)`'.

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Progress

Given the magnitude of a vector p = 20; what is the magnitude of vector p divided by 5 ?
20;twenty
20
5;five
5
4;four
4
1;one;by
1/4
The answer is "4".
Given the magnitude of a vector p, what is the magnitude of vector p divided by magnitude of vector p?
1;one
1
magnitude
magnitude of vector p
minus one;-1
minus 1
minus
minus magnitude of vector p
The answer is "1"
Given two vectors p and q, how can you verify if the vectors are in the same direction?
directional;cosines
directional cosines should be equal
components;along;axes
components along axes should be equal
The answer is 'Directional Cosines should be equal' along the respective axes.
Given two vectors p and p divided by 2, are these in the same direction?
different
Different directions
opposite
Opposite directions
same
Same direction
The answer is "Same Direction"
It is shown that magnitude of vector p divided by magnitude of vector p is 1 ;; and direction of vector p divided by magnitude of vector p is same as that of vector p.
Unit vector in the direction of a vector is the vector divided by its magnitude.
Unit Vector along a Vector: The unit vector along a given vector p is given by ;; hat p = vector p divided by magnitude of vector p.
Find the unit vector along the direction of vector p = 2 i + 2 j + 2 k
1
2
3
The answer is "1 by square root 3 multiplied i + j + k".

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