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Question
Find the equation of a line passing through the points P (-1, 3, 2) and Q (-4, 2, -2). Also, if the point R (5, 5, λ) is collinear with the points P and Q, then find the value of λ.
Solution
Equation of the line passing through the points P (-1, 3, 2) and Q (-4, 2, -2) is
` (x+1)/(-1+ 4) = (y -3)/(3 - 2) = (z - 2)/(2 + 2)`
`(x + 1)/(3) = (y - 3)/(1) = (z - 2)/(4)`
∵ Point R ( 5, 5, λ) lies on it,
`(5 + 1)/(3) = (5 - 3)/(1) = (λ - 2)/(4) ⇒ λ = 10`
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