# Find components of vector C from vectors A and B

## 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 $$C_{y} = 6.1$$

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