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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 projections of OP on the axis are 135,195,265 respectively, then P divides QR in the ratio

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

The correct option is D 3:2
Since, ¯¯¯¯¯¯¯¯OP has projections 135,195,265 on the coordinate axes
¯¯¯¯¯¯¯¯OP=135^i+195^j+265^k
Suppose P divides the line segment joining of Q(2,2,4) and R(3,5,6) in the ratio λ:1
then the position vector of P is
(3λ+2λ+1)^i+(5λ+2λ+1)^j+(6λ+4λ+1)^k
135^i+195^j+265^k=(3λ+2λ+1)^i+(5λ+2λ+1)^j+(6λ+4λ+1)^k
λ=3/2
Required ratio in which P divides QR is 3:2

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