First slide

Introduction to 3-D Geometry

Question

$If the points (5, 4, 2), (8, k, - 7) and (6, 2, - 1) are collinear, then k =$

Moderate

A

$- 2$
B

$2$
C

$10$
D

$1$

Solution

The direction ratios of the line joining the first two points and the direction ratios of the line joining the last two points are as below
3,k-4,-9 and -2,2-k,6
If the above lines are coincident, then the above ratios are in proportion
$- \frac{3}{2} = \frac{k - 4}{2 - k} = - \frac{3}{2} 2 k - 8 = - 6 + 3 k k = - 2$

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