Question

If vector a = i - j + 7k and vector b = 5i - j + λk, then find the value of λ, so that vector(a + b) and vector(a - b) are perpendicular vectors.

Answer 1

Given that vector a = i - j + 7k and vector b = 5i - j + λk

∴ vector(a + b) = i - j + 7k + 5i - j + λk = 6i - 2j + (7 + λ)k

and vector(a - b)= i - j + 7k + 5i + j - λk = - 4i + (7 - λ)k

Now, vector(a + b) and vector(a - b) are perpendicular vectors

⇒ vector(a + b) x vector(a - b) = 0

⇒ (6i - 2j + (7 + λ)k) x (-4i + (7 - λ)k) = 0

⇒ - 24 + 0 + (7 + λ)(7 - λ) = 0

⇒ - 24 + 49 - λ2 = 0 ⇒ λ2 = 25 ⇒ λ = ± 5