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

Updated On: Jul 7, 2022
  • 6
  • 7
  • $\frac{22}{7}$
  • 3
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The Correct Option is C

Solution and Explanation

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] $
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Notes on Distance of a Point From a Line

Concepts Used:

Distance of a Point From a Line

The length of the perpendicular drawn from the point to the line is the distance of a point from a line. The shortest difference between a point and a line is the distance between them. To move a point on the line it measures the minimum distance or length required.

To Find the Distance Between two points:

The following steps can be used to calculate the distance between two points using the given coordinates: 

  • A(m1,n1) and B(m2,n2) are the coordinates of the two given points in the coordinate plane.
  • The distance formula for the calculation of the distance between the two points is, d = √(m2 - m1)2 + (n2 - n1)2
  • Finally, the given solution will be expressed in proper units.

Note: If the two points are in a 3D plane, we can use the 3D distance formula, d = √(m2 - m1)2 + (n2 - n1)2 + (o2 - o1)2.

Read More: Distance Formula