SOLUTION: Find K so that the vectors [4,-3] and [k,-6] (a) point in the same direction (b) are perpendicular

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Question 147049: Find K so that the vectors [4,-3] and [k,-6] (a) point in the same direction
(b) are perpendicular
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
a)Point in the same direction means the vectors are scaled versions of each other.
In other words, the x components are in the same proportion as the y components.
4%2Fk=%28-3%29%2F%28-6%29
k=8
b)Perpendicular vectors have a dot product equal to zero.
A:[4,-3]
B:[k,-6]
A%2AB=4%2Ak%2B%28-3%29%28-6%29=0
4%2Ak%2B18=0
4%2Ak=-18
k=-18%2F4
k=-9%2F2
drawing%28+300%2C+300%2C+-6%2C+6%2C+-6%2C+6%2Cgrid%28+1+%29%2Cblue%28line%280%2C0%2C-4.5%2C-6%29%29%2Cgreen%28line%28+0%2C0%2C+4%2C+-3%29%29%29
Graphical check of the answer.