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Q.

A vector $\large 3\hat i+4\hat j$ rotates about its tail through an angle 37^o in anticlockwise direction then the new vector is

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a

$3\hat i - 4\hat j$

b

$5\hat i$

c

$\large - 3\hat i + 4\hat j$

d

$5\hat j$

answer is C.

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Detailed Solution

$\overline A = 3\widehat i + 4\widehat j;\;\left| {\overline A } \right| = \sqrt {25} = 5$
The direction of vector with x-axis is Q = Tan^-1(4/3) = 53⁰
$\therefore$ Total angle is 90⁰ in anticlock wise direction means new vector is along y-axis i.e. = $5\hat j$

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