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asked ago in Mathematics by (21.7k points)

The equation of the line passing through (–4, –3, –1), parallel to the plane x + 2y – z – 5 = 0 and intersecting the line x + 1/-3 = y - 3/2 = z - 2/-1 is

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Correct option  (4)  x + 4/3 = y- 3/-1 = z - 1/1

Explanation:

Let P.O.I. of line is  (–3λ – 1, 2λ + 3, – λ + 2)

Direction cosines of line is  (–3λ + 3, 2λ, –λ + 1). Since this line is parallel to x + 2y – z = 5

hence dot product is zero.

(–3λ + 3)1 + 4λ –1(– λ + 1) = 0

λ = –1

Hence direction cosines 6, –2, 2 are

x + 4/3 = y- 3/-1 = z - 1/1

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