Answer:
vector equation and parametric equations for the line are;
r(t) = < 1, 0, 9 > + t< 1, 3, 1 >
x(t),y(t),z(t) = < 1 + t, 3t, 9 + t >
Step-by-step explanation:
Given the data in the question;
Plane = x + 3y + z = 5
Normal of pane ⇒ <a> = < 1, 3, 1 >
As line is perpendicular to pane, Line is parallel to normal of plane.
⇒ Direction ratio of line < 1, 3, 1 >
Also line passes through < 1, 0, 9 >
so
r(t) = < 1, 0, 9 > + t< 1, 3, 1 >
Also,
(x-1)/1 = (y-0)/3 = (z-9)/1 = t
⇒ (x-1)/1 =t, (y-0)/3 = t, (z-9)/1 = t
⇒ x = 1 + t, y = 3t, z = 9 + t
⇒ x(t),y(t),z(t) = < 1 + t, 3t, 9 + t >
Therefore, vector equation and parametric equations for the line are;
r(t) = < 1, 0, 9 > + t< 1, 3, 1 >
x(t),y(t),z(t) = < 1 + t, 3t, 9 + t >
