Solar panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.
A simple application of vector dot and cross products lets us predict the amount of electrical power the panels can produce.
A surveyor on the sidewalk uses his instruments to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture shown above, suppose the points are labeled counter clockwise from the roof corner nearest the camera in units of meters:
$ P_1(6, 8, 4)$, $P_2(21, 8, 4)$, $P_3(21, 16, 10)$ and $P_4(6, 16, 10)$.
Problem 1
What are the components to the two edge vectors defined by
$A = P_2-P-1$ and $B = P_4-P_1$.
Write the vector in standard notation with x, y and z being the coordinate unit vectors.
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