Question

Find the equation of the line that passes through the point(1,2,3)and is parallel to the vector 3$\hat i$+2$\hat j$-2$\hat k$.

Answer 1

It is given that the line passes through the point A(1,2,3).

Therefore, the position vector through A is

$\vec a$=$\hat i$+2$\hat j$+3$\hat k$, $\vec b$=3$\hat i$+2$\hat j$-2$\hat k$

It is known that the line that passes through point A and is parallel to $\vec b$ is given by $\vec r$=$\vec a$+λ$\vec b$, where λ is a constant.

⇒$\hat i$+2$\hat j$+3$\hat k$+λ+(3$\hat i$+2$\hat j$-2$\hat k$)

This is the required equation of the line.