Question

For an observer on positive y axis , a vector 3î is rotated by 90° anticlockwise in x-z plane .The new vector will be
(1)3 k
(2)3 j
(3)3(-j)
(4)3(-k)​

Answer 1

The new vector will be 3$\dhat{k}$.

Explanation:

1. Here observer is on Y -axis, it is meaning that vector is rotate with respect to Y- axis.

2. Original vector is 3$\dhat{i}$, it's magnitude is unit 3.

3. Now it is rotate with anticlockwise $\theta$.

   New vector = $r\cos \theta \hat{i}+r\sin \theta \hat{k}$     ...a)

4. Where in equation a)

   r is magnitude of vector, which is 3.

  $\theta$ is angle of rotation in anti clock wise, which is 90°

5. Now equation a)  is

    New vector = $3\cos 90\hat{i}+3\sin 90 \hat{k}$

  So new vector = 3$\dhat{k}$