(4) You are doing some calculations about a solar panel on the roof of a house as shown in the image below. To help you with your work, you have determined the components for two vectors ā = (-10,0, 6) and b = (0, 4, 0) on the solar panel. Additionally, the current position of the sun means that the sunshine is coming at a direction given by the unit vector 5= ( ,1 2 2, (a) Find a unit vector i that is normal (orthogonal) to the solar panel. This vector represents the direction where maximum sunlight is absorbed.
(4) You are doing some calculations about a solar panel on the roof of a house as shown in the image below. To help you with your work, you have determined the components for two vectors ā = (-10,0, 6) and b = (0, 4, 0) on the solar panel. Additionally, the current position of the sun means that the sunshine is coming at a direction given by the unit vector 5= ( ,1 2 2, (a) Find a unit vector i that is normal (orthogonal) to the solar panel. This vector represents the direction where maximum sunlight is absorbed.
(4) You are doing some calculations about a solar panel on the roof of a house as shown in the image below. To help you with your work, you have determined the components for two vectors ā = (-10,0, 6) and b = (0, 4, 0) on the solar panel. Additionally, the current position of the sun means that the sunshine is coming at a direction given by the unit vector 5= ( ,1 2 2, (a) Find a unit vector i that is normal (orthogonal) to the solar panel. This vector represents the direction where maximum sunlight is absorbed.
You are doing some calculations about a solar panel on the roof of a house as shown in the image below. To help you with your work, you have determined the components for two vectors a=<-10,0,6> and vector b=<0,4,0> on the solar panel. Additionally, the current position of the sun means that the sunshine is coming at a direction given by the unit vector s=<1/3,2/3,-2/3>
*I hope you answer all question and wrote detail
Transcribed Image Text:(b) Determine how much of the sunlight \( \vec{s} = \left\langle \frac{1}{3}, \frac{2}{3}, -\frac{2}{3} \right\rangle \) is pointing in the direction of greatest solar power.
(c) What do you think your solution to (b) means in context of the solar panels?
(d) What would you do to find a vector that represents the sunlight that is pointing in the direction of greatest solar power? You do not need to find the vector, just explain the process or write out the computation you would complete.
Transcribed Image Text:**Title: Calculating Optimal Direction for Solar Panel Sunlight Absorption**
**Overview:**
In this problem, we analyze a solar panel installed on the roof of a house. The goal is to determine a unit vector normal to the solar panel surface, which signifies the direction of maximum sunlight absorption.
**Vectors and Sunshine Direction:**
- **Vectors on the Solar Panel:**
- \(\mathbf{a} = \langle -10, 0, 6 \rangle\)
- \(\mathbf{b} = \langle 0, 4, 0 \rangle\)
- **Sunlight Direction:**
- \(\mathbf{s} = \left\langle \frac{1}{3}, \frac{2}{3}, -\frac{2}{3} \right\rangle\)
**Problem Statement:**
(a) Determine a unit vector \(\mathbf{v}\) that is orthogonal (normal) to the solar panel. The calculated vector will point in the direction of maximum sunlight absorption.
**Note:**
After finding \(\mathbf{v}\), if its z-component is positive, adjust the vector by changing the signs of all its components. This ensures the vector points into the solar panel rather than away from it.
**Diagram Explanation:**
The image features:
- A house with a tilted roof, showing a rectangular solar panel on top.
- Vectors \(\mathbf{a}\) and \(\mathbf{b}\) depicted with arrows on the solar panel surface, illustrating directions along the panel plane.
- A sun icon with rays, indicating sunlight approaching the panel, represented by the vector \(\mathbf{s}\).
This setup helps understand the geometric relationships and calculations needed to optimize the solar panel's orientation for sunlight capture.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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