Question

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.

Answer 1

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.