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Question

If the foot of the perpendicular drawn from the point (1,0,3) on a line passing through (α,7,1) is (53,73,173), then α is equal to

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Solution

Given points P(1,0,3) and Q(53,73,173)

Direction ratios of PQ:(23,73,83)
Direction ratios of line L:(α53,773,1173)
=(3α53,143,143)

As line L is perpendicular to PQ,
so, (23)(3α53)+(73)(143)+(83)(143)=0

6α10+98112=0
6α=24α=4

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