Question

Cartesian equation of line passing through $(2,2,-3)$ and $(1,3,5)$ is ________

• A. $\frac{x-2}{-1}=\frac{y-2}{1}=\frac{z+3}{8}$
• B. $\frac{x-2}{1}=\frac{y-2}{1}=\frac{z+3}{8}$
• C. $\frac{x-1}{7}=\frac{y-3}{2}=\frac{z-5}{8}$
• D. $\frac{x-1}{2}=\frac{y-3}{2}=\frac{z-5}{-3}$

Answer 1

The correct option is A $\frac{x-2}{-1}=\frac{y-2}{1}=\frac{z+3}{8}$

$\to A\left(\overline{a}\right)=(2,2,-3)=(x_1,y_1,z_1)$
$B\left(\overline{b}\right)=(1,3,5)=(x_2,y_2,z_2)$
Now cartesian equation of line passes from $A\left(\overline{a}\right)$ and $B\left(\overline{b}\right)$ is as follows
$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$
$\therefore \frac{x-2}{-1}=\frac{y-2}{1}=\frac{z+3}{8}$
Required equation of a line which passes through $(2,2,-3)$ and having direction $(-1,1,8)$ is,
$\frac{x-2}{-1}=\frac{y-2}{1}=\frac{z+3}{8}$