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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