Question

Find the scalar equation for the plane passing through the point \( P=(1,4,-3) \) and containing the line \( L \) defined by \[ \begin{array}{l} x=-1-3 t \\ y=5 t \\ z=-5+4 t \\ 0=0 \end{array} \]

Answer 1

The scalar equation for the plane passing through the point P=(1,4,-3) and containing the line L defined by x=-1-3t, y=5t, and z=-5+4t, along with the condition 0=0 is 3x - 5y - 4z + 22 = 0.

Step-by-step explanation:

To find the scalar equation for the plane passing through point P=(1,4,-3) and containing the line L, we need to determine the normal vector to the plane. The direction vector of line L is given by