The projection of the line segment joining the points (- 1, 0, 3) and (2, 5, 1) on the line whose direction ratios are (6, 2, 3) is

A
6
B
7
C
$\frac{22}{7}$
D
3

Solution:

Direction cosines of the line are

$\begin{array}{l} (\frac{6}{\sqrt{\{(6)^{2} + (2)^{2} + (3)^{2}\}}}, \frac{2}{\sqrt{\{(6)^{2} + (2)^{2} + (3)^{2}\}}} \\ \frac{3}{\sqrt{\{(6)^{2} + (2)^{2} + (3)^{2}\}}}) i.e., (\frac{6}{7}, \frac{2}{7}, \frac{3}{7}) \end{array}$

$∴$ Projection of the line segment joining the points on the given line= $\begin{aligned} \frac{6}{7} (2 + 1) + \frac{2}{7} (5 - 0) + \frac{3}{7} (1 - 3) = \frac{22}{7} \\ [l (x_{2} - x_{1}) + m (y_{2} - y_{1}) + n (z_{2} - z_{1})] \end{aligned}$

The projection of the line segment joining the points $(- 1, 0, 3)$ and $(2, 5, 1)$ on the line whose direction ratios are $(6, 2, 3)$ is

Solution:

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