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=−i−2j+kS(1,2,5)=→s=i+2j+5k←→PQ=→q−→p=(4i+7j+8k)−(2i+3j+4k)=2i+4j+4k...(i)←→RQ=→s−→r=(i+2j+5k)−(−i−2j+k)=2i+4j+4k...(ii)∴←→PQ=←→RS From (i & ii) ∴points are parallal.