Find components of vector C from vectors A and B

[casemeister06]

Homework Statement

Given vectors \vec{A} = 5.0\hat{i} - 6.5\hat{j} and \vec{B} = -3.5\hat{i}= 7.0\hat{j}. Vector \vec{C} lies in the xy-plane. Vector \vec{C} is perpendicular to \vec{A} and the scalar product of \vec{C} with \vec{B} is 15.0. Find the vector components of \vec{C}.

Homework Equations

\vec{A}{\cdot}\vec{C} = 0
\vec{B}{\cdot}\vec{C} = 15

\vec{B}{\cdot}\vec{C}=B_{i}C_{i}+B_{j}C_{j}=15
\vec{B}{\cdot}\vec{C}=-3.5C_{i}+7.0C_{j}=15

\vec{A}{\cdot}\vec{C}=A_{i}C_{i}+A_{j}C_{j}=0

The Attempt at a Solution

Since the vectors A and C are perpendicular
\vec{A}{\cdot}\vec{C} = 0
Then,
\vec{A}{\cdot}\vec{C}=A_{i}C_{i}+A_{j}C_{j}=0
\vec{A}{\cdot}\vec{C}=5.0_{i}C_{i}-6.5_{j}C_{j}=0
C_{j}=\frac{5.0_{i}C{i}}{6.5}

Plug in C_{j} into the other scalar equation and solve for C_{i}. Basic substitution. However I keep getting the wrong answer. Am I approaching the problem incorrectly or is my algebra wrong?

The correct answer is C_{x} = 8.0 and C_{y} = 6.1

 

[rl.bhat]

Hi casemeister06, welcome to PF.
-3.5Ci + 7Cj = 15...(1)
5.0Ci - 6.5Cj = 0...(2)
Multiply by 0.7 to eq. (2) and add it to eq.(1) and solve for Cj.

 

[casemeister06]

Yeah, I don't know what I was doing, but I got it right now. I think I was messing up on my algebra or something. Thanks for the help.