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Given vec(P)=3hat(i)-4hat(j). Which of t...

Given `vec(P)=3hat(i)-4hat(j)`. Which of the following is perpendicular to `vec(P)`?

A

`3hat(i)`

B

`4hat(j)`

C

`4hat(i)+3hat(j)`

D

`4hat(i)-3hat(j)`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(P)` is the fourth quadrant. `4hat(i)+3hat(j)` is in the first quadrant. Clearly, `4hat(i)+3hat(j)` can be perpendicular to `vec(P)`. For confirmation, let us check whether their dot product is zero.
`(3hat(i)-4hat(j)).(4hat(i)+3hat(j))=12-12=0`
This shows that `4hat(i)+3hat(j)` is perpenduicular to `3hat(i)+4hat(j)`.
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