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

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

Step-by-step 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`.