Question

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 (13, 2, 9), B (5, 5, 9), C (0, 8, 5), and D (8, 2, 11) (see the following figure). n = AB x AD is a vector perpendicular to the surface of the solar panels. Assume s = 1/?3 i + 1/?3 j + 1/?3 k points toward the Sun at a particular time of the day and the flow of solar energy is F = 900s. 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). Determine the angle of elevation of the Sun above the solar panel. Express the answer in degrees. (Hint: The angle between vectors n and s and the angle of elevation are complementary (add to 90 degrees))

          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 (13, 2, 9), B (5, 5, 9), C (0, 8, 5), and D (8, 2, 11) (see the following figure).
n = AB x AD is a vector perpendicular to the surface of the solar panels. Assume s = 1/?3 i + 1/?3 j + 1/?3 k points toward the Sun at a particular time of the day and the flow of solar energy is F = 900s. 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).
Determine the angle of elevation of the Sun above the solar panel. Express the answer in degrees. (Hint: The angle between vectors n and s and the angle of elevation are complementary (add to 90 degrees))

Show more…

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 (13, 2, 9), B (5, 5, 9), C (0, 8, 5), and D (8, 2, 11) (see the following figure).
n = AB x AD is a vector perpendicular to the surface of the solar panels. Assume s = 1/?3 i + 1/?3 j + 1/?3 k points toward the Sun at a particular time of the day and the flow of solar energy is F = 900s. 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).
Determine the angle of elevation of the Sun above the solar panel. Express the answer in degrees. (Hint: The angle between vectors n and s and the angle of elevation are complementary (add to 90 degrees))

Added by Carol P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/24/2022

Step 1

Step 1: Compute the vector AB: The vector AB is given by the coordinates of points A and B: AB = B - A = (5-13)i + (5-2)j + (9-9)k AB = -8i + 3j Show more…

Show all steps

lock

Thanks for your feedback!

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 (13, 2, 9), B (5, 5, 9), C (0, 8, 5), and D (8, 2, 11) (see the following figure). n = AB x AD is a vector perpendicular to the surface of the solar panels. Assume s = 1/sqrt(3)i + 1/sqrt(3)j + 1/sqrt(3)k points toward the Sun at a particular time of the day and the flow of solar energy is F = 900s. 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). Determine the angle of elevation of the Sun above the solar panel. Express the answer in degrees. (Hint: The angle between vectors n and s and the angle of elevation are complementary (add to 90 degrees))

Play audio

Feedback

Powered by NumerAI

Madhur L and 89 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

0:00 Hello everyone.

00:02 We need to compute the electrical power for that first we need to compute the vector n which is given to be ab vector cross product ad vector so we are given with the point a is 1329 b is given to be 5 5 9 and the point d is given to be 8 to 11.

00:38 So using this first let us compute ab vector.

00:43 This is nothing but the distance between the points a and b.

00:48 So this will give us 5 minus 13i plus 5 minus 2 j plus 9m minus 9 k.

01:06 So this is minus 8i plus 3j.

01:11 Similarly, we can compute ad vector that is equal to 8 minus 13 i plus 2 minus 2 j plus 11 minus 9 k clearly this is equal to 5i plus 2k using this, now we can compute our vector n, that is equal to determinant i .j .k.

01:51 Minus 8, 3, 0, 5 ,02.

01:59 So if we simplify this determinant, we'll get the n vector.

02:06 So that is, n vector is equal to 6i plus 16 j.

02:15 Minus 15 k.

02:21 So now it is easy for us to compute the electrical power p.

02:26 So that is given by the dot product of f into n vector.

02:36 Here f is equal to 900 s so this can be written as 900 by 900 by root 3 into i plus j plus k.

02:54 So now let us take the drought product of f and n to compute p.

03:01 So p is equal to 900 by root 3 into icap plus j cap plus k cap into 6i plus 16 j j minus 15 k k so further simplifying this we would get 900 by root 3 into 6 plus 16 minus 15.

03:37 Clearly the electrical power p is equal to 3 ,637 .31 watts...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later