You can
put this solution on YOUR website!to get the unit vector you need to get the magnitude of the vector and then divide each measure used by the magnitude.
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in your problem, you have (i,j,k) = (3,1,2)
magnitude =
=
=
=
.
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you take each measure and divide by the magnitude to get (
,
,
)
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you simplify the fraction by multiplying each by
to get (
,
,
) which can be simplified further to get (
,
,
) although I think I would want to keep all denominators the same.
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your answer will either be (
,
,
) or (
,
,
)
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this is a unit vector because the magnitude is now 1 as shown by the following equation:
magnitude of vector =
-----
this becomes
which becomes
which becomes
which becomes
.
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A unit vector in the opposite direction would have the same values only negatives of whatever is there.
In this case, your unit vector in the opposite direction should be (
,
,
)
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Note that keeping the denominator the same seemed like a good idea especially when verifying that the magnitude is 1.
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