Find the unit normal vector to the plane with positive first coordinate. Using t

Question

Find the unit normal vector to the plane with positive first coordinate.

Using this unit normal vector, find the scalar equation of the plane.

Note: You can earn partial credit on this problem.

Consider the plane through the point (4, 5, -2) and parallel to the plane 4x - 5y - 3z = 2. Find the unit normal vector to the plane with positive first coordinate. Using this unit normal vector, find the scalar equation of the plane. Multiply both sides by 50 and simplify to get the standard equation of the plane.

Explanation / Answer

n = <4/sqrt(50),-5/sqrt(50),-3/sqrt(50)>

(4/sqrt(50))(x-4)-(5/sqrt(50))(y-5)-(3/sqrt(50))(z+2)=0

4x-5y-3z=-3

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