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Question: If x co-ordinates of a point P of line joining the points \(Q ( 2,2,1 )\) and \(R ( 5,2 , - 2 )\)i...

If x co-ordinates of a point P of line joining the points Q(2,2,1)Q ( 2,2,1 ) and R(5,2,−2)R ( 5,2 , - 2 )is 4, then the z-coordinates of P is

A

– 2

B

–1

C

1

D

2

Answer

–1

Explanation

Solution

Suppose P divides QR in the ratio λ:1\lambda : 1.

Then co-ordinates of P are (5λ+2λ+1,λ+2λ+1,−2λ+1λ+1)\left( \frac { 5 \lambda + 2 } { \lambda + 1 } , \frac { \lambda + 2 } { \lambda + 1 } , \frac { - 2 \lambda + 1 } { \lambda + 1 } \right) .

It is given that the x-coordinate of P is 4. i.e.,5λ+2λ+1=4\frac { 5 \lambda + 2 } { \lambda + 1 } = 4

⇒ λ=2\lambda = 2

So, z-coordinate of P is −2λ+1λ+1=−4+12+1=−1\frac { - 2 \lambda + 1 } { \lambda + 1 } = \frac { - 4 + 1 } { 2 + 1 } = - 1.