Find the image of the point in the line .

Answer

Given: Equation of line is .

To find: image of point

Formula Used: Equation of a line is

Vector form:

Cartesian form:

where is a point on the line and with being the direction ratios of the line.

If 2 lines of direction ratios and are perpendicular, then Mid-point of line segment joining and is

\left(\frac{x_{1}-x_{2}}{2}, \frac{y_{1}-y_{2}}{2}, \frac{z_{1}-z_{2}}{2}\right)

Explanation:

Let

\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}=\lambda

So the foot of the perpendicular is

The direction ratios of the perpendicular is

\begin{array}{l}

(5 \lambda-3-0):(2 \lambda+1-2):(3 \lambda-4-3) \\

\Rightarrow(5 \lambda-3):(2 \lambda-1):(3 \lambda-7)

\end{array}

Direction ratio of the line is