Vectors
posted by Victor on .
Given vectors A = 4.8i + 6.8j and B = 9.6i + 6.7j, determine the vector C that lies in the xy plane perpendicular to B and whose dot product with A is 20.0.

let the vector C = [a,b]
then using the dot product condition:
4.8a + 6.8b = 20
or
12a  17b = 50
slope of vector B is 6.7/9.6 or 67/96
slope of vector C is b/a
since the are perpendicualr
b/a =  96/67
b = 96a/67
subbing back into first equation,
12a  17(96a/67) = 50
solving this I got
a = 1675/1218
and then back into the first ...
b = 400/203
so vector C = [1675/1218, 400/203]
I will leave it up to you to check it out, it does work.