The value of t for which the line x−12=y−3t=z−11passes through the point 1,3,1and 3,1,2is

The value of $t$ for which the line $\frac{x - 1}{2} = \frac{y - 3}{t} = \frac{z - 1}{1}$ passes through the point $(1, 3, 1)$ and $(3, 1, 2)$ is

A
1
B
2
C
$- 2$
D
0

Solution:

The direction ratios of the line joining the points $(1, 3, 1)$ and $(3, 1, 2)$ is $2, - 2, 1$

Comparing the direction ration of the line $2, t, 1$ , the value of $t$ is $- 2$

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