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Given two vectors vec(A)=3hat(i)+4hat(j)...

Given two vectors `vec(A)=3hat(i)+4hat(j)` and `vec(B)=hat(i)+hat(j).theta` is the angle between `vec(A)` and `vec(B)`. Which of the following statements is/are correct?

A

`|vecA|costheta((hati+hatj)/(sqrt(2)))` is the component of `vecA ` along `vecB` .

B

`|vecA|sintheta((hati-hatj)/(sqrt(2)))` is the component of `barA` perpendicular to `vecB`

C

`|vecA|costheta((hati-hatj)/(sqrt(2)))` is the component of `vecA` along `barB` .

D

`|vecA|sintheta((hati+hatj)/(sqrt(2)))` is the component of `vecA` perpendicular to `vecB` .

Text Solution

Verified by Experts

The correct Answer is:
A, B
Component of `vecA` along `vecB` is `|vecA| cos theta hatB` for `theta` being the angle between the vectors. Also `hatB= (hati+hatj)/(sqrt(2))` . So choice (a) is correct.
The vector `( hati-hatj)` is perpendicular to the vector `(hati+hatj)`
So the other resolved component is
`|vecA|sin theta= ((hati-hatj)/(sqrt(2)))`
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