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in Three-dimensional geometry by (36.3k points)

A line with positive direction cosines passes through the point P(2, –1, 2) and makes equal angles with the co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

(a) 1

(b) √2

(c) √3

(d) 2

1 Answer

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by (33.0k points)
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Best answer

Answer is (c) √3

Let the equation of the line passing through P(2, –1, 2) and makes equal angles with the co-ordinate axes is

Thus, the point Q is (3, 0, 3). Therefore, the length of PQ = √((3 – 2)2 (0 + 1)2 + (3 – 2)2)  = √3 

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