Question

How do you find the unit vector parallel to the resultant of the vectors A= 2i - 6j -3k and B = 4i + 3j- k?

Answer 1

The Reqd. Unit Vector `=(6/sqrt61,-3/sqrt61,-4/sqrt61)`.

Explanation:

Let a non-null vector `vecx` be given. Then, a unit vector parallel to `vecx` is

denoted by `hatx` and is defined by,

`hatx=vecx/||vecx||`

`vecA=2hati-6hatj-3hatk=(2,-6,-3), &, vecB=(4,3,-1)`.

Hence, the Resultant of `vecA and vecB`, is `vecA+vecB`, & is,

`vecA+vecB=(2,-6,-3)+(4,3,-1)=(2+4,-6+3,-3-1)=(6,-3,-4)`

`:. ||vecA+vecB||=sqrt{6^2+(-3)^2+(-4)^2}=sqrt61`

Hence, the Reqd. Unit Vector `=(vecA+vecB)/||vecA+vecB||`

`=1/sqrt61(6,-3,-4)=(6/sqrt61,-3/sqrt61,-4/sqrt61)`.