Question

You are given two vectors, one pointing in the x direction and the other pointing in the y direction. Is it possible to find a third vector so that the sum of the three vectors is equal to zero? yes yes, but only because the vectors are perpendicular no only if the two vectors have the same magnitude A points in the-X direction with a magnitude of 12, what is the y component of A? Enter an exact number C is 95 units in the x direction. D is 135 units in the y direction. Find the vector so that the sum C+D+E-o units at measured counterclockwise from the +x axis. Submit Answer Save Progress

Answer 1

The y component of A^rightarrow will be A^rightarrow_y = A sin 0 = 12 times 0 A_y = 0 now C^rightarrow + D^rightarrow + E^rightarrow = 0 E^rightarrow = -(C + d^rightarrow) C^rightarrow = 95 units By parallelogram law, Vertical-bar C^rightarrow + D^rightarrow Vertical-bar = squareroot C^2 + D^2 + 2 CD cos 90 = squareroot C^2 + D^2 = squareroot 95^2 + 13562 = 165.07 now, a_1 E^rightarrow is opposite to (C^rightarrow + D^rightarrow) the angle will be theta = r + tan^-1(135/95) = 180 + 54.86 = 234.88 degree = 234.86 degree