First slide

Introduction to 3-D Geometry

Question

If the points (-1, 3, 2), (4, 2, -2) arid (5, 5, l,) are collinear, then $λ =$

Moderate

A

10
B

-10
C

-8
D

8

Solution

Let (5, 5, $λ$ ) divide the segment joining (-1, 3,2) and (4,2, -2) in the ratio k : l.
$\begin{array}{l} ∴ (\frac{- 4 k - 1}{k + 1}, \frac{2 k + 3}{k + 1}, \frac{- 2 k + 2}{k + 1}) \equiv (5, 5, λ) \\ So, - 4 k - 1 = 5 k + 5 and 2 k + 3 = 5 k + 5 \\ ∴ k = - 2 / 3 \end{array}$
So, comparing z-coordinate with k = -2/3, we get
$\begin{array}{l} 4 / 3 + 2 = λ / 3 \\ ∴ λ = 10 \end{array}$

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