What are the x and y components of a vector a in the xy plane if its direction i

Question

What are the x and y components of a vector a in the xy plane if its direction is 240 degree The x component of a vector A is -33.0 m and the y component is +39.0 m. What is the magnitude of A? What is the angle between the direction of A and the positive direction of x? counterclockwise from the +x-axis Two vectors are given by a = (6.0 m)i - (2.5 m) j + (1.0 m)k and b = (-1.0 m)i + (1.0 m) j + (3.0 m)k. In unit-vector notation, find the following. a + b = a - b = a third vector c such that a - b + c = 0

Explanation / Answer

The magnitude of A =. ( (x^2) + (y^2) ) put x = - 33 y= 39

A = 51.088 m

Angle theta = arctan (y/x) = arctan (39/- 33) = - 49.76 degrees since y is positive x is negative it is in direction of 2nd quadrant therefore to calculate angle from horizontal CCW 180 - 49.76 = 130.24 degrees.

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