Let x → , y → and z → be three vectors each of magnitude 2 and the angle between each pair of them is π 3 . If a → is a non - zero vector perpendicular to x → and y → × z → and b → is a non - zero vector perpendicular to y → and z → × x → , then

Step-by-step solution

a → is in direction of x → × y → × z → i.e., x → . z → y → - x → . y → z → ⇒ a → = λ 1 2 × 1 2 y → - z → a → = λ 1 y → - z → ........(i) Now a → . y → = λ 1 y → . y → - y → . z → = λ 1 2 - 1 ⇒ λ 1 = a → . y → ........(ii) From (i) and (ii), a → = a → . y → y → - z → Similarly, b → = b → . z → z → - x → Now, a → . b → = a → . y → b → . z → y → - z → . z → - x → = a → . y → b → . z → 1 - 1 - 2 + 1 = - a → . y → b → . z →