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Question

Show that the lines PQ are RQ parallel where P,Q,R,S are the points (2,3,4),(4,7,8),(1,2,1) and (1,2,5) respectively.

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Solution

P(2,3,4)=p=2i+3j+4kQ(4,7,8)=q=4i+7j+8kR(1,2,1)=r=i2j+kS(1,2,5)=s=i+2j+5kPQ=qp=(4i+7j+8k)(2i+3j+4k)=2i+4j+4k...(i)RQ=sr=(i+2j+5k)(i2j+k)=2i+4j+4k...(ii)PQ=RS
From (i & ii)
points are parallal.

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