Find the equation of line in vector and cartesian form that passes through the point with position vector (2i - j + 4k)

Question

Find the equation of line in vector and cartesian form that passes through the point with position vector \(2\hat{i}-\hat{j}+4\hat{k}\) and is in the direction \(\hat{i}+2\hat{j}-\hat{k}\)

Answer 1

P.V. of a point of line = \(2\hat{i}-\hat{j}+4\hat{k}.\)

\(\Rightarrow\) the coordinate of that point = (2, -1, 4)

Therefore vector equation of the plane is

Also its cartesian form is

Therefore required equation in cartesian form is

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