00:01
In this problem, we are given with some points.
00:03
They are 2 comma minus 1 comma minus 4 and there is a plane that contains some points 5 comma minus 2 comma minus 4 comma 3 comma 0 minus 5 comma 1.
00:24
We need to find the distance between this point and the plane containing these 3 .0 .0.
00:30
Minus 5 comma 1.
00:30
Find the plain equation.
00:32
Therefore, the plain equation where the formula for the plain equation is determinant of x minus x1, x2 minus x1, x3 minus x1, y minus y 1, y2 minus x1, y2 minus x1, y3 minus y1.
00:53
Z minus z1, z2 minus z1, and z3 minus z1 is equals to 0, where the points are x1, x1, x1, x2, y, 2, z2 and x3 by 3 by 3.
01:09
Similarly, we'll substitute here, this is x1, y, 1, z1, x2, y2, z2, x3, y, 3, z3, which implies x minus 5, y minus of minus 2, z minus of minus 4.
01:30
This is 3 minus 5, 0 minus of minus 2, minus 1 minus of minus 4.
01:39
Next one is 0 minus 5 minus 5 minus of minus 2 and 1 minus of minus 4.
01:48
This is the determinant equivalent equals to 0.
01:53
Now here, which implies x minus 5, y plus 2 and z plus 4...