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

Answer:

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

Explanation:

To find the magnitude, you use the Pitagorean theorem:

$||V|| = \sqrt{x^2 + y^2}= \sqrt{(-26.5)^2 + (43)^2} = 33.86 units$

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.:

$tan(\alpha) = \frac{y}{x} \\\alpha = tan^{-1}(\frac{43}{-26.5})= 180 - tan^{-1}(\frac{43}{26.5}) = 121.64$° or, 58.36° in the second quadrant