If the vectors veca = hati- hatj+2 hatk, vecb = 2 hati+4 hatj+ hatk and vecc = λ hati+ hatj+μ hatk are mutually orthogonal, then (λ, μ) =

Question

If the vectors veca = hati- hatj+2 hatk, vecb = 2 hati+4 hatj+ hatk and vecc = λ hati+ hatj+μ hatk are mutually orthogonal, then (λ, μ) =  (A) (2, -3) (B) (-2, 3) (C) (3, -2) (D) (-3, 2)

Tardigrade Admin · Accepted Answer

veca ⋅ vecb = 0, vecb ⋅ vecc = 0, vecc ⋅ veca = 0 ⇒ 2λ + 4 + μ = 0 λ - 1+2μ = 0 Solving we get: λ = -3, μ = 2

Q. If the vectors $a = \hat{i} - \hat{j} + 2 \hat{k}, b = 2 \hat{i} + 4 \hat{j} + \hat{k}$ and $c = λ \hat{i} + \hat{j} + μ \hat{k}$ are mutually orthogonal, then $(λ, μ) =$

(2, -3)

(-2, 3)

(3, -2)

(-3, 2)

$a \cdot b = 0, b \cdot c = 0, c \cdot a = 0$
$\Rightarrow 2 λ + 4 + μ = 0 λ - 1 + 2 μ = 0$
Solving we get: $λ = - 3, μ = 2$

Q. If the vectors a=i^−j^​+2k^,b=2i^+4j^​+k^ and c=λi^+j^​+μk^ are mutually orthogonal, then (λ,μ)=