Question

if = 2i-3j+k and B= 3j+nk and if A and B are perpendicular then the value of n is

Answer 1

Here is your answer......
A = 2i + 3j + k
B = 3j + nk

Given A ⊥ B ⇒ angle b/w A & B, θ = 90°

A . B = 0    (Dot product)


|A| = √(2² + 3² + 1²) = √14
|B| = √(3² + n²) = √(9+n)

|A||B| cosθ = |A||B| cos 90° = 0
⇒ √(14) × √(9+n) = 0
⇒ 126 + 14n = 0
⇒ n = -9

∴The value of n is -9

I hope it helps you ^_^

Answer 2

A = 2i - 3j + k
B = 3j + nk

A and B are perpendicular. Their dot product should be zero

A · B = (2i - 3j + k) · (0i + 3j + nk)
0 = 0 - 9 + n
n = 9