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Question

If A(2,1, 3), B(2, -3, 4) , C(-1, 2 , 7) are the three points ; find a point D such that |AB|=12|CD|andAB||CD.

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Solution

AB=12CDorAB=12CDAB=4ˆj+ˆk2(4ˆj+ˆk)=DC2(4ˆj+ˆk)=CD8ˆj+2ˆkˆi+2ˆj+7ˆk=ˆ08ˆj+2ˆk+ˆi2ˆj7ˆk=ˆ0D=ˆi6ˆj+9ˆkˆi10ˆj5ˆk=ˆ0orD=ˆi+10ˆj+5ˆk

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