Question

Find the cartesian equation of the plane passing through the points A (0, 0, 0) and B (3, –1, 2) and parallel to the line \(\frac{x-4}{1}=\frac{y+3}{-4}=\frac{z+1}{7}.\)

Answer 1

Equation of plane is given by

Given plane passes through (0, 0, 0)

Plane (i), passes through (3, -1, 2)

\(\therefore\) 3a - b + 2c = 0 ......(ii)

Also, plane (i) is parallel to the line

Eliminating a, b, c from equations (i), (ii) and (iii), we get

\(\Rightarrow x - 19y - 11z = 0,\) which is the required equation.