The value of λ ∈ R such that (x, y, z) ≠(0,0,0) and ( hati+ hatj+3 hatk) x+(3 hati-3 hatj+ hatk) y+(-4 hati+5 hatj) z=λ(x hati+y hatj+z hatk) can be

Question

The value of λ ∈ R such that (x, y, z) ≠(0,0,0) and ( hati+ hatj+3 hatk) x+(3 hati-3 hatj+ hatk) y+(-4 hati+5 hatj) z=λ(x hati+y hatj+z hatk) can be (A) 1 (B) -1 (C) 0 (D) 2

Tardigrade Admin · Accepted Answer

|1-λ 3 -4 1 -3-λ 5 3 1 -λ|=0 gives λ(λ+1)2=0

Q. The value of $λ \in R$ such that $(x, y, z) \neq = (0, 0, 0)$ and $(\hat{i} + \hat{j} + 3 \hat{k}) x + (3 \hat{i} - 3 \hat{j} + \hat{k}) y + (- 4 \hat{i} + 5 \hat{j}) z = λ (x \hat{i} + y \hat{j} + z \hat{k})$ can be

1

-1

0

2

$∣ ∣ 1 - λ 13 3 - 3 - λ 1 - 4 5 - λ ∣ ∣ = 0$ gives $λ (λ + 1)^{2} = 0$

Q. The value of λ∈R such that (x,y,z)=(0,0,0) and (i^+j^​+3k^)x+(3i^−3j^​+k^)y+(−4i^+5j^​)z=λ(xi^+yj^​+zk^) can be

1

-1

0

2

∣∣​1−λ13​3−3−λ1​−45−λ​∣∣​=0 gives λ(λ+1)2=0

Q. The value of $λ \in R$ such that $(x, y, z) \neq = (0, 0, 0)$ and $(\hat{i} + \hat{j} + 3 \hat{k}) x + (3 \hat{i} - 3 \hat{j} + \hat{k}) y + (- 4 \hat{i} + 5 \hat{j}) z = λ (x \hat{i} + y \hat{j} + z \hat{k})$ can be

$∣ ∣ 1 - λ 13 3 - 3 - λ 1 - 4 5 - λ ∣ ∣ = 0$ gives $λ (λ + 1)^{2} = 0$