The value of λ such that (x,y,z)≠(0,0,0) and i→+j→+3k→x+3i→-3j→+k→y+-4i→+5j→z=λxi→+yj→+zk→ are

1-λx+3y-4z=0 x+(-3-λ)y+5z=0 3x+y-λz=0 If (x,y,z)≠(0,0,0), then 1-λ3-41-3-λ531-λ=0

The value of λ such that (x,y,z)≠(0,0,0) and i→+j→+3k→x+3i→-3j→+k→y+-4i→+5j→z=λxi→+yj→+zk→ are

1-λx+3y-4z=0 x+(-3-λ)y+5z=0 3x+y-λz=0 If (x,y,z)≠(0,0,0), then 1-λ3-41-3-λ531-λ=0

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The value of $λ$ such that
$(x, y, z) \neq (0, 0, 0)$ and
$(\vec{i} + \vec{j} + \vec{3 k}) x + (\vec{3 i} - 3 \vec{j} + \vec{k}) y + (\vec{- 4 i} + 5 \vec{j}) z = λ (\vec{x i} + \vec{y j} + \vec{z k})$ are

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$(0, 1)$

$0, - 1$

$1, - 1$

$0, 1, - 1$

answer is B.

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$(1 - λ) x + 3 y - 4 z = 0 x + (- 3 - λ) y + 5 z = 0 3 x + y - λ z = 0 I f (x, y, z) \neq (0, 0, 0), t h e n |\begin{matrix} 1 - λ & 3 & - 4 \\ 1 & - 3 - λ & 5 \\ 3 & 1 & - λ \end{matrix}| = 0$

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The value of λ such that (x,y,z)≠(0,0,0) and i→+j→+3k→x+3i→-3j→+k→y+-4i→+5j→z=λxi→+yj→+zk→ are

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The value of $λ$ such that
$(x, y, z) \neq (0, 0, 0)$ and
$(\vec{i} + \vec{j} + \vec{3 k}) x + (\vec{3 i} - 3 \vec{j} + \vec{k}) y + (\vec{- 4 i} + 5 \vec{j}) z = λ (\vec{x i} + \vec{y j} + \vec{z k})$ are