Question

Find the separation vector r from the source point (2,8,7) to the field point (4,6,8). Determine its magnitude (r), and construct the unit vector ˆr.

Answer 1

magnitude =3 unit vector
`(2i-2j+k)/(3)`

Explanation:

We have given source point
`(x_1,y_1,z_1)=(2,8,7)`

And the field point
`(x_2,y_2,z_2)=(4,6,8)`

Resultant vector
`=(x_2-x_1)i+(y_2-y_1)j+(z_2-z_1)k=(4-2)i+(6-8)j+(8-7)k=2i-2j+k`

The resultant vector
`=2i-2j+k`

Magnitude of the vector
`=√(2^2+2^2+1^2)=3`

Now we have to find the unit vector

So unit vector
`=(2i-2j+k)/(3)`