Problem 1B-01: Position vectors originated from one reference point
Use the summation and subtraction of position vectors of the first kind as defined in Topic 1-7 to perform the following operations.
(a) Draw position vectors expressed in rectangular coordinates,
A = (5, 3), B = (-1, 2), C = (0, -2),on x-y plane.
(b) Draw A + B +3C on the same graph as (a).
(c) Position vector D originates from the origin, has a length of 3 and points exactly northwest. Draw it on the x-y plane. Express D in rectangular coordinates.
(d) E and F both originate from the origin. E points north-north-east, forming an angle of 60 degree with x-axis, and the magnitude of E, |E|, is 3. F points south-east-east, forming an angle of -30 degree with the x-axis, and |F| = 4. Express both position vectors in rectangular coordinates.
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(a) The solutions are drawn in the following graph
(b) A+B+3C = (5+(-1)+3·(0), 3+2+3·(-2)) = (4, -1).
The position vector is shown in the following graph.
(c) The position vector D is shown in the figure. From the picture we get
(d) Position vectors E and F are drawn in the following picture.
In the rectangular coordinate representations, we get
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