Two points in a rectangular coordinate system have the coordinates (4.04, 3.87)

Question

Two points in a rectangular coordinate system have the coordinates (4.04, 3.87) and (- 280, 4.00), respectively, with centimeters as units. Determine the distance between these points. Answer: Two vectors are given by a = 1.7i - 8.0j and b = - 17.7i + 8.0 j. What is the magnitude of a? Answer: What is the angle between vector b and the positive x-axis? Answer: Enter "deg" as the for angles in degrees: do nod the circle symbol! What is the magnitude of the vector a + b? Answer: An airplane's initial location relative to the control tower is given by vector A (A = 39.0 km) that points 37.0 degree north of west. It travels to a new position, given by vector B relative to the control tower (B = 58.0 km. with a direction 73.0 degree west of south). Draw a diagram, with the x axis pointing east and the y axis pointing north. Calculate the x and y components of vector B. Enter find B_ then B_ . Answer 1 of 2: __________ Answer 2 of 2: __________ What are the x and y components of the airplane's displacement d = B - A? Enter first d_ then d_ . Answer 1 of 2: __________ Answer 2 of 2: __________

Explanation / Answer

3. distance = sqrt[ (4.04 + 2.80)^2 + (3.87 - 4)^2]

= 6.84

4. magnitude of a = sqrt[ 1.7^2 + 8^2]

= 8.18

5. angle = 180 - tan^-1(8/17.7) = 156 deg

6. a + b = -16 i + 0j

magnitude = 16

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