Case-Study 2: Read the following passage and answer the questions given below
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 surveyor uses his instrument to determine the coordinates of the four corners of a roof where solarpanels are to be mounted.In the picture, suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P1 (6,8,4), P2 (21,8,4),P3 (21,16,10) and P4 (6,16,10).
Answer the following questions using the above information.
i. What are the components to the two edge vectors defined by $\vec{A} = PV of P_{2} - PV of P_{1} and \vec{B} = PV of P_{4} - PV of P_{1} ?$ (Where, PV stands for position vector).
ii. Write the vector in standard notation with $\hat{i}, \hat{j}$ and $\hat{k}$ , where $\hat{i}, \hat{j}$ , and $\hat{k}$ are the unit vectors along the three axes.
iii. What are the magnitudes of the vectors $\vec{A}$ and $\vec{B}$ and in what units?

Question

Case-Study 2: Read the following passage and answer the questions given below
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 surveyor uses his instrument to determine the coordinates of the four corners of a roof where solarpanels are to be mounted.In the picture, suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P1 (6,8,4), P2 (21,8,4),P3 (21,16,10) and P4 (6,16,10).
Answer the following questions using the above information.
i. What are the components to the two edge vectors defined by $\vec{A} = PV of P_{2} - PV of P_{1} and \vec{B} = PV of P_{4} - PV of P_{1} ?$ (Where, PV stands for position vector).
ii. Write the vector in standard notation with $\hat{i}, \hat{j}$ and $\hat{k}$ , where $\hat{i}, \hat{j}$ , and $\hat{k}$ are the unit vectors along the three axes.
iii. What are the magnitudes of the vectors $\vec{A}$ and $\vec{B}$ and in what units?

Infinity Learn · Accepted Answer

(i) A→=PV of P2-PV of P1 =21i^+8j^+4k^-6j^+8j^+4k^ =15i^+0j^+0k^ ∴ Components of A→ are 15, 0, 0. and B→=PV of P4-PV of P1 =6i^+16j^+10k^-6i^+8j^+4k^ =0i^+8j^+6k^ ∴ Components of B→ are 0, 8, 6.(ii) Clearly, from sol (i). Vector in standard notation with i^, j^ and k^ are A→=15i^+0j^+0k^ and B→=0i^+8j^+6k^ (iii) A→=(15)2+(0)2+(0)2 =(15)2=15 units and B→=(0)2+(8)2+(6)2=0+64+36 = 100=10 units

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