Question

Find the value λ for which the vectors `vec"a"` and `vec"b"` are perpendicular, where `vec"a" = 2hat"i" + 4hat"j" - hat"k"` and `vec"b" = 3hat"i" - 2hat"j" + lambdahat"k"`

Answer 1

When `vec"a"` and `vec"b"` are ⊥^r then `vec"a"*vec"b"` = 0

`vec"a"` ⊥^r  `vec"b"` ⇒ `vec"a" * vec"b"` = 0

(2)(3) + (4)(– 2) + (– 1)(λ) = 0

6 – 8 – λ = 0

– λ – 2 = 0

⇒ – λ = 2

⇒ λ = – 2