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

1 Answer
Alan P.
Jul 26, 2016

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))

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