Question

Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° east of north. The resultant vector + is given by

Answer 1

Answer:

The resultant vector is $\vec R = \vec A + \vec B = 7.196\,i + 6.464\,j$.

Explanation:

First, each vector is determined in terms of absolute coordinates:

6-meter vector with direction: 30º north of east.

$\vec A = (6\,m)\cdot (\cos30^{\circ} \,i + \sin 30^{\circ}\,j)$

$\vec A = 5.196\,i + 3\,j$

4-meter vector with direction: 30º east of north.

$\vec B = (4\,m)\cdot (\cos 60^{\circ}\,i + \sin 60^{\circ}\,j)$

$\vec B = 2\,i + 3.464\,j$

The resultant vector is obtaining by sum of components:

$\vec R = \vec A + \vec B = 7.196\,i + 6.464\,j$

The resultant vector is $\vec R = \vec A + \vec B = 7.196\,i + 6.464\,j$.