Find a nonzero vector orthogonal to the plane through the points: =(0,0,1), =(−2,3,4), =(−2,2,0).

The nonzero vector orthogonal to the plane is <-9,-8,2>.

Step-by-step explanation:

Consider the given points are P=(0,0,1), Q=(−2,3,4), R=(−2,2,0).

The nonzero vector orthogonal to the plane through the points P,Q, and R is

Expand along row 1.

Therefore, the nonzero vector orthogonal to the plane is <-9,-8,2>.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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