Question

Find the cartesion equation of the plane passing through the point $(-2,1,3)$ and perpendicular to the vector $3i+j+5k.$

Answer 1

plane passes through (-2,1,3)

perpendicular vector is $3\hat{i}+\hat{j}+5\hat{k}$

normal vector will be 3$\hat{i}+\hat{j}+5\hat{k}$

Cartesian equation -

(x+2)$\times$3+(y-1)$\times$1+(z-3)$\times$5=0

3x+6+y-1+5z-15=0

3x+y+5z-10=0

3x+y+5z=10