ISRO 2014- vector {mech}

Question

Angle made between vector C = 2i- 3j+ 4k and the Z-axis is

a) 4 /√29

b) $sin^ {- 1}$ 4 /√29

c) $cos^ {-1}$ 4 /√29

d) $tan ^{-1 }$4 /√29

Answer 1

We can use dot product here. A.B = |A||B|*cos x

Now B= k and A.B = 4, |A| =√29 and |B| =1 so answer is x = cos^-1(4/√29) (option C)