If →a = ^i − ^j + 7^k and →b = 5^i − ^j + λ^k, then find the value of λ, so that →a + →b and →a − →b are perpendicular vectors.

→a = →i − →j + 7→k
→b = 5→i − →j + λ→k
→a + →b = 6→i − 2→j + (7 + λ)→k
→a − →b = -4→i + 0→j + (7 − λ)→k
Given →a + →b and →a − →b are perpendicular, then
→a + →b . →a − →b = 0
(6→i − 2→j + (7 + λ)→k) . (-4→i + 0→j + (7 − λ)→k) = 0
6(-4) + 0(-2) + (7 + λ)(7 − λ) = 0
-24 + 49 − λ^2 = 0
λ^2 = 25
Squaring on both the sides, we get
λ = ±5