Question

A vector has an x-component of -26.5 and a y-component of 43 units. Find magnitude and direction of vector

Answer 1

The vector has a magnitude of 33.86 units and a direction of 121.64°.

Step-by-step explanation:

To find the magnitude, you use the Pitagorean theorem:

`||V|| = √(x^2 + y^2)= √((-26.5)^2 + (43)^2) = 33.86 units`

In order to find the direction, you can use trigonometry. You have to keep in mind, that as the y component of the vector is positive and the x component is negative, the vector must have an angle between 90 and 180°, or in the second quadrant of the plane.:

`tan(\alpha) = (y)/(x) \\\alpha = tan^(-1)((43)/(-26.5))= 180 - tan^(-1)((43)/(26.5)) = 121.64`° or, 58.36° in the second quadrant