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1 vector solutions - liu(ql744 vec rev chiu(56565 This...

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This print-out should have 30 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 7) 3.0 points A proton is located at: 4 × 10 - 10 m , - 7 × 10 - 10 m , 5 × 10 - 10 m . Find r , the location of the proton from the origin where r = r x , r y , r z . What is r x in meters? Your answer must be within ± 5.0% Correct answer: 4 × 10 - 10 m. Explanation: The position of the proton is the vector from the origin to the location of the proton. In this case: 4 × 10 - 10 m , - 7 × 10 - 10 m , 5 × 10 - 10 m 002 (part 2 of 7) 3.0 points What is r y in meters? Your answer must be within ± 5.0% Correct answer: - 7 × 10 - 10 m. Explanation: The position of the proton is the vector from the origin to the location of the proton. In this case: 4 × 10 - 10 m , - 7 × 10 - 10 m , 5 × 10 - 10 m 003 (part 3 of 7) 3.0 points What is r z in meters? Your answer must be within ± 5.0% Correct answer: 5 × 10 - 10 m. Explanation: The position of the proton is the vector from the origin to the location of the proton. In this case: 4 × 10 - 10 m , - 7 × 10 - 10 m , 5 × 10 - 10 m 004 (part 4 of 7) 2.0 points What is | r | in meters? Your answer must be within ± 5.0% Correct answer: 9 . 48683 × 10 - 10 m. Explanation: The magnitude of r is found by: | r | = r 2 x + r 2 y + r 2 z where: r x = 4 × 10 - 10 m r y = - 7 × 10 - 10 m r z = 5 × 10 - 10 m therefore: | r | = 9 . 48683 × 10 - 10 m 005 (part 5 of 7) 3.0 points What is ˆ r x , the x component of the unit vector in the direction of r ? Your answer must be within ± 5.0% Correct answer: 0 . 421637. Explanation: The unit vector has the form: ˆ r = r | r | . This means that the x component of the unit vector is: ˆ r x = r x | r | = 4 × 10 - 10 m 9 . 48683 × 10 - 10 m = 0 . 421637 006 (part 6 of 7) 3.0 points What is ˆ r y , the y component of the unit vector in the direction of r ? Your answer must be within ± 5.0% Correct answer: - 0 . 737865. Explanation: The unit vector has the form: ˆ r = r | r | .
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This means that the y component of the unit vector is: ˆ r y = r y | r | = - 7 × 10 - 10 m 9 . 48683 × 10 - 10 m = - 0 . 737865 007 (part 7 of 7) 3.0 points What is ˆ r z , the z component of the unit vector in the direction of r ? Your answer must be within ± 5.0% Correct answer: 0 . 527046. Explanation: The unit vector has the form: ˆ r = r | r | . This means that the z component of the unit vector is: ˆ r z = r z | r | = 5 × 10 - 10 m 9 . 48683 × 10 - 10 m = 0 . 527046 008 (part 1 of 5) 10.0 points A planet is located at P = - 4 × 10 10 , 8 × 10 10 , - 5 × 10 10 . A star is located at S = 7 × 10 10 , - 6 × 10 10 , 5 × 10 10 . What is R , the vector pointing from the star to the planet? 1. R = 9 × 10 10 , - 1 . 4 × 10 11 , 6 × 10 10 2. R = 8 × 10 10 , - 1 . 6 × 10 11 , 6 × 10 10 3. R = 1 . 1 × 10 11 , - 1 . 4 × 10 11 , 1 × 10 11 correct 4. R = 6 × 10 10 , - 1 . 1 × 10 11 , 9 × 10 10 5. R = 9 × 10 10 , - 1 . 6 × 10 11 , 1 × 10 11 Explanation: This is a vector subtraction problem. To find R , we subtract S - P by respective com- ponents: S x - P x = 7 × 10 10 - ( - 4 × 10 10 ) = 1 . 1 × 10 11 S y - P y = - 6 × 10 10 + 8 × 10 10 = - 1 . 4 × 10 11 S z - P z = 5 × 10 10 + ( - 5 × 10 10 ) = 1 × 10 11 So R = S - P =
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