First slide

Introduction to 3-D Geometry

Question

If the line joining the points $(k, 1, 2), (3, 4, 6)$ is parallel to the line joining the points $(- 4, 3, - 6), (5, 12, l)$ then $(k, l) =$

Moderate

A

(-2,7)
B

(0, 6)
C

(0, -6)
D

(2, -7)

Solution

D.r’s of a line joining $(k, 1, 2), (3, 4, 6)$ are $(3 - k, 3, 4)$
D.r’s of a line joining $(- 4, 3, - 6), (5, 12, l)$ are $(9, 9, l + 6)$
Since these two lines are parallel
$\frac{3 - k}{9} = \frac{3}{9} = \frac{4}{l + 6}$ , $\Rightarrow k = 0, l = 6$

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