Use lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 2, 5).

The point on the plane x − 2y + 3z = 6 that is closest to the point (0, 2, 5) is.

Let (x,y,z) be the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 2, 5).Then

The gradient of f and g are

Δ=

Δ

Setting Δf=kΔg

k(1,-2,3)

2x=k,2(y-3)=-2k,2(z-5)=3k

Solving we get the point

Therefore the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 2, 5) is.

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175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

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