The co-ordinates of three points A,B,C are respectively (2, 1, 3), (-1, 2, 4) and (0, 2, 1). Determine the quation of plane ABC and its point of intersection with line $r = (i - j + k) + λ (2 i + k) .$

(7, - 1, 4) .

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(- 7, 1, 4) .

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(7, 1, - 4) .

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None of these

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Solution

The correct option is A $(7, - 1, 4) .$
The equation of plane through given points is $r - (3 i + 8 j + k) = 17.$
Solving with given line on putting the value of $r$ from line in the equation of plane,
we get $- 4 + λ (7) = 17$
$∴ 7 λ = 21$ $\Rightarrow λ = 3.$
Hence the point of intersection is $7 i - j + 4 k$ or $(7, - 1, 4) .$

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