Find the value of λso that the four points, A, B, C and D with position vectors 4i^+5j^+k^,−j^−k^,3i^+λj^+4k^and −4i^+4j^+4k^respectively are coplanar.

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Find the value of that the four points, A, B, C and D with po

Question

Find the value of $λ$ so that the four points, A, B, C and D with position vectors $4 \hat{i} + 5 \hat{j} + \hat{k}, - \hat{j} - \hat{k}, 3 \hat{i} + λ \hat{j} + 4 \hat{k}$ and $- 4 \hat{i} + 4 \hat{j} + 4 \hat{k}$ respectively are coplanar.

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Lucas Discussed

Find the value of

λ

so that the four points, A, B, C and D with position vectors

4 \hat{i} + 5 \hat{j} + \hat{k}, - \hat{j} - \hat{k}, 3 \hat{i} + λ \hat{j} + 4 \hat{k}

and

- 4 \hat{i} + 4 \hat{j} + 4 \hat{k}

respectively are coplanar.

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Question Text

Find the value of

λ

so that the four points, A, B, C and D with position vectors

4 \hat{i} + 5 \hat{j} + \hat{k}, - \hat{j} - \hat{k}, 3 \hat{i} + λ \hat{j} + 4 \hat{k}

and

- 4 \hat{i} + 4 \hat{j} + 4 \hat{k}

respectively are coplanar.