Question

How to find a vector from magnitude and direction?

Answer 1

To find a vector from its magnitude and direction, use trigonometry to determine the x-component and y-component of the vector. Then, use the components to find the magnitude and direction of the vector using the Pythagorean theorem and inverse tangent function.

Step-by-step explanation:

To find a vector from its magnitude and direction, you can use trigonometry. First, determine the x-component and y-component of the vector using the given magnitude and direction. Then, use the components to find the magnitude and direction of the vector. For example, if you have a vector with magnitude 5 and direction 30 degrees above the positive x-axis, you would calculate the x-component as 5 * cos(30) and the y-component as 5 * sin(30). Finally, you can use the components to find the magnitude and direction of the vector by using the Pythagorean theorem and the inverse tangent function, respectively.

Answer 2

Suppose that the coordinates of the vector are (3, 4). You can find the angle theta as the tan–1(4/3) = 53 degrees. So if you have a vector given by the coordinates (3, 4), its magnitude is 5, and its angle is 53 degrees.