Two vectors are given by and

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

Problem

Two vectors are given by

\vec A = 2\hat i - \hat j + k\,\hat k

and

\vec B = k\,\hat i + 2\hat j + 3\hat k

, where

k

is a real number. (i) Write the mathematical condition for the two vectors to be perpendicular. (ii) Determine all possible values of

k

that satisfy the condition obtained in part (i). (iii) For each value of

k

found in part (ii), calculate the magnitude of the vector product

\vec A \times \vec B

and state the direction of

\vec A \times \vec B

with respect to

\vec A

and

\vec B

. Comment on how your results in parts (i) and (iii) are consistent with the geometrical meaning of the products involved.