Question

The Cartesian equation of the line passing through the point $(2,-1,4)$ and parallel to the vector $\overline{i}+\overline{j}-2\overline{k}$ is

• A. $\frac{x-2}{1}=\frac{y+1}{1}=\frac{z-4}{-2}$
• B. $\frac{x+2}{1}=\frac{y-1}{1}=\frac{z-4}{-2}$
• C. $\frac{x-2}{2}=\frac{y+1}{1}=\frac{z-4}{-2}$
• D. $\frac{x+2}{1}=\frac{y-1}{1}=\frac{z+4}{-2}$

Answer 1

The correct option is A $\frac{x-2}{1}=\frac{y+1}{1}=\frac{z-4}{-2}$

Equation a line passing through a point $(x,y,z)$ and parallel to a line with direction ratios $a,b,c$ is $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$

The line passes through $(2,-1,4)$

$x_1=2,y_1=-1,z_1=4$

In line $\hat{i}+\hat{j}-2\hat{k},a=1,b=1,c=2$

Equation of line in Cartesian form is

$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$

$\frac{x-2}{1}=\frac{y+1}{1}=\frac{z-4}{2}$

$\Rightarrow \frac{x-2}{1}=\frac{y+1}{1}=\frac{z-4}{-2}$

So option $\left(A\right)$ is correct.