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Question

If P(x,y,z) is a point on the line segment joining Q(2,2,4) and R(3,5,6) such that the projection of −−→OP on the axes are 135,195,265 respectively, then P divides QR in ratio

A
1:3
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B
2:3
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C
3:2
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D
3:1
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Solution

The correct option is C 3:2

Since OP has projection 135,195 and 265 on the coordinate axes, therefore OP=135i+195j+265k

Let P divides the join of Q(2,2,4) and R(3,5,6) in the ratio λ:1.

The position vector of P is (3λ+2λ+1)i+(5λ+2λ+1)j+(6λ+4λ+1)k

135i+195j+265k=(3λ+2λ+1)i+(5λ+2λ+1)j+(6λ+4λ+1)k

3λ+2λ+1=135,5λ+2λ+1=195,6λ+4λ+1=265

λ=32


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