Let , where is a real number, and let…

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let

\vec a = x\mathbf i + 3\mathbf j + 4\mathbf k

, where

x

is a real number, and let

\vec b = 2\mathbf i - \mathbf j + \mathbf k

. (i) If

\bigl|\vec a \times \vec b\bigr| = 10\sqrt{3}

, determine all possible values of

x

. (ii) For each value of

x

found in part (i), find every unit vector that is perpendicular to both

\vec a

and

\vec b