calculus Cartesian planes

Question

Answer 1

Note that both lines "start" at the same point, and the 2 lines go in different directions. (This guarantees that the 2 lines make a plane).

Therefore, we can use the cross-product to determine the "direction" of the plane and the starting point to get the location of the plane.

The determinant of

i j k

5 -4 6

2 -3 -4

is

34i + 32j -7k

Now, plug in the starting point.

34x + 32y -7z = 34(4) + 32(4) -7(5) = 229

34x + 32y - 7z = 229