If two vectors A = 4 i ^ + n j ^ + 2 k ^ and B = 2 i ^ + 2 j ^ − k ^ are mutually perpendicular to each other then value of 'n' is

Question

If two vectors A = 4 i ^ + n j ^ ​ + 2 k ^ and B = 2 i ^ + 2 j ^ ​ − k ^ are mutually perpendicular to each other then value of 'n' is

TestHub · Accepted Answer

For two vectors to be mutually perpendicular, their dot product must be zero.

$A \cdot B = 0$

$(4 \hat{i} + n \hat{j} + 2 \hat{k}) \cdot (2 \hat{i} + 2 \hat{j} - \hat{k}) = 0$

$(4) (2) + (n) (2) + (2) (- 1) = 0$

$8 + 2 n - 2 = 0$

$2 n + 6 = 0$

$n = - 3$

Answer: $- 3$

Physics - Vectors Question with Solution | TestHub

Options:

Doubts & Discussion