First slide

Vectors

Question

A vector $2 \hat{i} + 2 \hat{j}$ rotated about its tail through an angle $45^{\circ}$ in clockwise direction. Then the new vector is

Moderate

A

$2 \sqrt{2} \hat{j}$
B

$2 \hat{j}$
C

$2 \hat{i}$
D

$2 \sqrt{2} \hat{i}$

Solution

If a vector is rotated its magnitude does not change but direction changes .
$G i v e n v e c t o r i s m a k i n g 45^{0} w i t h x a x i s . A f t e r r o t a t i o n o f 45^{0} i n c l o c k w i s e d i r e c t i o n, i t w i l l b e c o m e p a r a l l e l t o x a x i s w i t h o u t c h a n g e i n i t s m a g n i t u d e . S o, n e w v e c t o r = 2 \sqrt{2} \hat{i}$

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