Find the parametric equations for the line through the point

Find the parametric equations for the line through the point (1,0,-1) and perpendicular to the plane 2x-3y+5z=35. Find the point where this line intersects the plane.

Solution

(x-1)/2=(y-0)/ (-3)= (z+1)/5 =t(let) then x=2t+1 y=-3t z=5t-1 b. point of intersection let be(2t+1,-3t,5t-1) then it satisfies the equation of plane so 2*(2t+1)-3*(-3t)+5*(5t-1)=35 so t=1 so point of intersection=(3,-3,4)