Let l be the line parametrized by x = 2 + 2t, y = 3t, z = −1 − t. (a) find a linear equation for the plane that is perpendicular to l and includes the point (2, 0, −1). (b) where does l intersect the plane x + 2y + 3z = 9?

Step-by-step explanation:

Given that L is a line parametrized by

The plane perpendicular to the line will have normal as this line and hence direction ratios of normal would be coefficient of t in x,y,z

i.e. (2,3,-1)

So equation of the plane would be of the form

Use the fact that the plane passes through (2,0,-1) and hence this point will satisfy this equation.

So equation is

b) Substitute general point of L in the plane to find the intersecting point

i.e. same point given.