Question

How do you find the sum of the unit vectors (2,2,7) and (5, -6, 2)?

Answer 1

Since the given `(2,2,7)` and `(5,-6,2)` are not unit vectors it is not clear what was intended by this question.

Explanation:

Possibility 1: Sum of the unit vectors with the same orientation as the given values
Since `sqrt(2^2+2^2+7^2)=sqrt(57)`
the unit vector corresponding to `(2,2,7)` is
`color(white)("XXX")(2/sqrt(57),2/sqrt(57),7/sqrt(57))`

Similarly the unit vector corresponding to `(5,-6,2)` is
`color(white)("XXX")(5/sqrt(65),-6/sqrt(65),2/sqrt(65))`

The sum of these unit vectors is
`color(white)("XXX")(2/sqrt(57)+5/sqrt(65),2/sqrt(57)-6/sqrt(65),7/sqrt(57)+2/sqrt(165))`
(these terms could be evaluated but given the question's ambiguity I have not bothered with the effort involved)

Possibility 2: Unit vector with the same orientation as the sum of the given vectors
`(2,2,7)+(5,-6,2)=(7,-4,9)`
with corresponding unit vector:
`color(white)("XXX")(7/sqrt(146),-4/sqrt(146),9/sqrt(146))`