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Q.

The value of k for which the points A(1,0,3), B(- 1,3,4), C(1,2,1) and D(k,2.5) are coplanar, is

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a

1

b

2

c

0

d

-1

answer is D.

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Detailed Solution

$\begin{array}{l} \vec{A B} = (- 2, 3, 1), \vec{A C} = (0, 2, - 2) \vec{A D} = (k - 1, 2, 2) \\ [\vec{A B} \vec{A C} \vec{A D}] = 0 \Rightarrow |\begin{array}{rrr} - 2 & 3 & 1 \\ 0 & 2 & - 2 \\ k - 1 & 2 & 2 \end{array}| = 0 \Rightarrow - 2 (4 + 4) - 3 (0 + 2 k - 2) + 1 (0 - 2 k + 2) = 0 \\ \Rightarrow - 8 k - 8 = 0 \Rightarrow k = - 1 \end{array}$

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