Question

Find the point at which the line r(t) = <4, -2, -7>t + <5, 2, -6> intersects the xz-plane?

Answer 1

To find the point at which the line intersects the xz-plane, substitute y = 0 into the equation of the line and solve for t. The line intersects the xz-plane at the point (4, 0, -7).

Step-by-step explanation:

To find the point at which the line intersects the xz-plane, we need to find the value of y when the line crosses the plane. The xz-plane is represented by the equation y = 0.

Substituting y = 0 into the equation of the line, we get:
r(t) = <4, -2, -7>t + <5, 2, -6>
Setting y = 0:
0 = -2t + 2
t = 1

So, the line intersects the xz-plane at the point (4, 0, -7).