Posted by vector length on Tuesday, August 23, 2011 at 12:38pm.
Find a vector that has the same direction as the given vector but has length 6.
‹2, 2, 4›
I know how to find a unit vector of this, but to find a vector in the same direction but length >1 I'm not sure how to determine the scalar multiple that will be needed. I know it will be >1 because the length of the current vector is sqrt(24) and l=6 would be l=sqrt(36).
I tried using the multiple of sqrt(36/24) but it didn;t work.
Any help would be appreciated.'

calculus  Reiny, Tuesday, August 23, 2011 at 12:54pm
a vector with the same direction is (1,1,2)
a unit vector in that same direction is
1/√6(1,1,2) or (1/√6, 1/√6, 2/√6)
so a vector 6 times that long is (6/√6, 6/√6, 12/√6)
or
(√6 , √6 , 2√6) after rationalizing the denominator.
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