For the line and the plane to be perpendicular, they have to meet at right angles
The equation for the plane is x + 2y + 3z= 26
From the complete question, we have:
Point = (5,0,7)
Plane perpendicular to ⟨1,2,3⟩
The general equation is:
a * x+b * y+c * z = d
So, we have:
d = 5 * 1 + 2 * 0 + 7 * 3
Evaluate
d = 26
Recall that:
d = 5 * 1 + 2 * 0 + 7 * 3
Replace the points with x, y and z.
So, we have:
d = x * 1 + 2 * y + 3 * z
Evaluate
d = x + 2y + 3z
So, we have:
d = x + 2y + 3z and d = 26
Equate both equations
x + 2y + 3z= 26
Hence the equation for the plane is x + 2y + 3z= 26
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