Question

Find the equation of line passing through the point $(4,5,6)$ and parallel to the vector $3\hat{i}+4\hat{j}+2\hat{k}$.

• A. $\frac{x-4}{3}=\frac{y-5}{4}=\frac{z-6}{2}$
• B. $\frac{x+4}{3}=\frac{y-5}{3}=\frac{z-6}{2}$
• C. $\frac{x+4}{3}=\frac{y+5}{4}=\frac{z+6}{2}$
• D. $\frac{x-4}{2}=\frac{y-5}{4}=\frac{z-6}{3}$

Answer 1

The correct option is A $\frac{x-4}{3}=\frac{y-5}{4}=\frac{z-6}{2}$

Line passes through the point $(4,5,6)$.

It is parallel to the vector $3\hat{i}+4\hat{j}+2\hat{k}$.

Hence, the equation of line is

$\frac{x-4}{3}=\frac{y-5}{4}=\frac{z-6}{2}$.