Question

We rotated vector A through an angle θ about its tail and we get a vector B. We rotated the same vector A through an angle θ about the centre of the vector and we get C as shown in the figure. Choose the correct option?

• A. B = C
• B. B C
• C. B = - C
• D. C = A

Answer 1

The correct option is A

B = C

Case I:

Let $\overrightarrow{A}$ makes an angle $\alpha$ with the positive direction of the x - axis, then $\overrightarrow{B}$ will make an angle of $(\alpha +\theta )$ with the

positive direction of the x axis.

Case II:

Let OA' be a line parallel to $\overrightarrow{A}$, then from the diagram it is obvious that the angle made by $O\overrightarrow{C}$ with the

positive direction of the x axis is $(\alpha +\theta )$.

$\therefore \overrightarrow{B}=\overrightarrow{C}$