Question

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

Answer 1

Answer: (C)

$\frac{22}{7}$

Answer 2

Direction cosines of the line are \frac{6}{\sqrt{\left\\{\left(6\right)^{2} + \left(2\right)^{2} + \left(3\right)^{2}\right\\} }} , \frac{2}{\sqrt{\left\\{\left(6\right)^{2} + \left(2\right)^{2} + \left(3\right)^{2}\right\\}}} , \frac{3}{\sqrt{\left\\{\left(6\right)^{2} + \left(2\right)^{2} +\left(3\right)^{2}\right\\}}} i .e., \frac{6}{7}, \frac{2}{7} , \frac{3}{7} $\therefore$ Projection of the line segment joining the points on the given line = $\frac{6}{7} \left(2+1\right) + \frac{2}{7}\left(5-0\right) + \frac{3}{7}\left(1-3\right)= \frac{22}{7}.$ $\left[l\left(x_{2 } - x_{1}\right) + m\left(y_{2} - y_{1}\right) + n \left(z_{2} - z_{1}\right)\right]$