?A solar panel is mounted on the roof of a house. The panel may be regarded as

Chapter 2, Problem 242

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A solar panel is mounted on the roof of a house. The panel may be regarded as positioned at the points of coordinates (in meters) A(8, 0, 0), B(8, 18, 0), C(0, 18, 8), and D(0, 0, 8) (see the following figure).

                                           

a. Find vector \(\mathbf{n}=\overrightarrow{A B} \times \overrightarrow{A D}\) perpendicular to the surface of the solar panels. Express the answer using standard unit vectors.

b. Assume unit vector \(\mathbf{s}=-\frac{1}{\sqrt{3}} \mathbf{i}+-\frac{1}{\sqrt{3}}-\mathbf{j}+-\frac{1}{\sqrt{3}} \mathbf{k}\) points toward the Sun at a particular time of the day and the flow of solar energy is F = 900s (in watts per square meter \(\left[\mathrm{W} / \mathrm{m}^{2}\right]\)). Find the predicted amount of electrical power the panel can produce, which is given by the dot product of vectors F and n (expressed in watts).

c. Determine the angle of elevation of the Sun above the solar panel. Express the answer in degrees rounded to the nearest whole number. (Hint: The angle between vectors n and s and the angle of elevation are complementary.)

Text Transcription:

n = overrightarrow AB times overrightarrow AD

s = 1/sqrt 3 i + 1/sqrt 3 - j + 1/sqrt 3 k

[W / m^2]