Question

You are given vectors A = 5.0i - 6.5j & B = -3.5i + 7.0j. A third vector C lies on the xy-plane. Vector C is perpendicular to vector A, & the scalar product of C with B is 15.0. From this information, find the components of vector C.

Answer 1

A=[5,-6.5]
B=[-3.5,7]

If A is perpendicular to C, then A.C=0, or
C=[6.5k, 5k]
(verify that A.C=0)

If in addition, C.B=15, we have
C.B=[6.5k,5k].[-3.5,7]
=35k-22.75k
=12.25k

But C.B=15, therefore 12.25k=15, =>
k=15/12.25=60/49

Therefore
C=[6.5k,5k]
=[390/49, 300/49]

Check my arithmetic and that the given conditions are satisfied.

Answer 2

thanks

Answer 3

you're welcome!

Answer 4

I don't understand the flow in the math here. Please help me understand this solution by "dumbing it down" a bit.