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Question
The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.
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Solution
Let the point P divide QR in the ratio λ : 1, then the co-ordinate of P are
`((5lambda + 2)/(lambda + 1), (lambda + 2)/(lambda + 1), (-2lambda + 1)/(lambda + 1))`
But x– coordinate of P is 4.
Therefore, `(5lambda + 2)/(lambda + 1)` = 4
⇒ λ = 2
Hence, the z-coordinate of P is `(-2lambda + 1)/(lambda + 1)` = –1.
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