Question

if a bar =i^+j^-2k^ and b bar =xi^+j^-3k^ are parpendicular then find x​

Answer 1

Answer -7

When two vectors are Perpendicular to each other, Their 'dot product's yields 0.

This is because cos(90°) = 0, which makes whole term 0.

Coming back to question,

$a= i + j - 2k \\ b = xi + j - 3k \\ \\ a.b = 0 \\ = > (1.x) + (1.1) + ( - 2.( - 3)) = 0 \\ = > x + 1 + 6 = 0 \\ = > x = - 7$

(Remember ' . ' represents multiplication between the values.)

Hope this helps!