The position vectors of the point A,B,CandDare3i^−2j^−k^,2i^+3j^−4k^,−i^+j^+2k^ and 4i^+5j^+λk^, respectively. If the points A,B,CandD lie on a plane, find the value of λ˙

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The position vectors of the point {A},{B},{C}{a}{n}{d}{D}{a}{r

Question

The position vectors of the point $A, B, C a n d D a r e 3 \hat{i} - 2 \hat{j} - \hat{k}, 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, - \hat{i} + \hat{j} + 2 \hat{k}$ and 4 $\hat{i} + 5 \hat{j} + λ \hat{k},$ respectively. If the points $A, B, C a n d D$ lie on a plane, find the value of $λ ˙$

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The position vectors of the point

A, B, C a n d D a r e 3 \hat{i} - 2 \hat{j} - \hat{k}, 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, - \hat{i} + \hat{j} + 2 \hat{k}

and 4

\hat{i} + 5 \hat{j} + λ \hat{k},

respectively. If the points

A, B, C a n d D

lie on a plane, find the value of

λ ˙

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Question Text

The position vectors of the point

A, B, C a n d D a r e 3 \hat{i} - 2 \hat{j} - \hat{k}, 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, - \hat{i} + \hat{j} + 2 \hat{k}

and 4

\hat{i} + 5 \hat{j} + λ \hat{k},

respectively. If the points

A, B, C a n d D

lie on a plane, find the value of

λ ˙