Find the values of λ such that x,y,z=(0,0,0)and(i^+j^+3k^)x+(3i^−3j^+k^)y+(−4i^+5j^)z=λ(xi^+yj^+zk^), where i^,j^,k^ are unit vector along coordinate axes.

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Find the values of such that {x},{y},{z}{({0},{0},{0})}{a}{n}

Question

Find the values of $λ$ such that $x, y, z \neq = (0, 0, 0) a n d (\hat{i} + \hat{j} + 3 \hat{k}) x + (3 \hat{i} - 3 \hat{j} + \hat{k}) y + (- 4 \hat{i} + 5 \hat{j}) z = λ (x \hat{i} + y \hat{j} + z \hat{k})$ , where $\hat{i}, \hat{j}, \hat{k}$ are unit vector along coordinate axes.

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Find the values of

λ

such that

x, y, z \neq = (0, 0, 0) a n d (\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})

, where

\hat{i}, \hat{j}, \hat{k}

are unit vector along coordinate axes.

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Question Text

Find the values of

λ

such that

x, y, z \neq = (0, 0, 0) a n d (\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})

, where

\hat{i}, \hat{j}, \hat{k}

are unit vector along coordinate axes.