Question

Find the value of λ for which the vectors (a and b) are perpendicular, where

(i) vector a = 2i + λj + k and vector b = i - 2j + 3k

(ii) vector a = 2i + 4j - k and vector b = 3i - 2j + λk

Answer 1

When vector (a and b) are ⊥^r then vector (a.b) = 0 

vector a ⊥^r vector b ⇒ vector (a.b) = 0 

(i) (2) (1) + (λ) (-2) + (1) (3) = 0 ⇒ λ = 5/2 

(ii) (2) (3) + (4) (-2) + (-1) (λ) = 0

6 – 8 – λ = 0 

-λ – 2 = 0 ⇒ -λ = 2 ⇒ λ = -2