For vectors and having magnitudes and respectively

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

For vectors

\vec A = A_x\hat i + A_y\hat j + A_z\hat k

and

\vec B = B_x\hat i + B_y\hat j + B_z\hat k

having magnitudes

A

and

B

respectively, which one of the following expressions gives

\cos\phi

, where

\phi

is the angle between the two vectors? (a)

\dfrac{|\vec A\times\vec B|}{AB}

(b)

\dfrac{A_xB_x + A_yB_y + A_zB_z}{A^{2}+B^{2}}

(c)

\dfrac{A_xB_x + A_yB_y + A_zB_z}{AB}

(d)

\dfrac{(A_x+A_y+A_z)(B_x+B_y+B_z)}{AB}