Solving Vector Problems: Homework Statement and Equations Explained

[cdlegendary]

Homework Statement

You are given vectors vec A= 4.6i - 6.6j and vec B= - 3.0i + 7.2j. A third vector vec C lies in the xy-plane. Vector vec C is perpendicular to vector vec A and the scalar product of vec C with vec B is 18.0. (the i and j are hat values, they have a ^ over them)

Homework Equations

C * B = 18
C * B = |C|*|B|cos(x)
A * C = 0, because they are parallel

The Attempt at a Solution

I used the two equations
(Cx)(Bx)+(Cy)(By) = 18
(Ax)(Cx)+(Ay)(Cy) = 0

but could not reach a solution. I would greatly appreciate some guidance

 

[jegues]

(Cx)(Bx)+(Cy)(By) = 18
(Ax)(Cx)+(Ay)(Cy) = 0

You are given Bx, By, Ax, Ay, so you simply have 2 equations with 2 unknowns which you can solve for by a number of ways.

 

[kerimek]

.I would first start by understanding the problem and the given information. It seems like you are given two vectors, A and B, and you are asked to find a third vector, C, that is perpendicular to A and has a scalar product of 18 with B.

To solve this problem, we can use the dot product formula: A * B = |A|*|B|cos(theta), where |A| and |B| are the magnitudes of the vectors and theta is the angle between them. Since we know that C is perpendicular to A, theta must be 90 degrees, making cos(theta) = 0.

Next, we can rewrite the given scalar product equation as C * B = |C|*|B|cos(theta) = |C|*|B|*0 = 0. This means that the dot product of C and B must be 0.

Using the dot product formula, we can expand the dot product of C and B as (Cx)(Bx)+(Cy)(By) = 0. We also know that C is perpendicular to A, so the dot product of C and A must also be 0. This gives us the equation (Cx)(Ax)+(Cy)(Ay) = 0.

Now, we have a system of two equations with two unknowns (Cx and Cy). We can solve for one variable in terms of the other and plug it into the other equation to solve for the remaining variable.

For example, we can solve for Cx in terms of Cy in the first equation: Cx = -(Cy)(By)/Bx. Then we can substitute this into the second equation, giving us -(Cy)(By)(Ax)+(Cy)(Ay) = 0. We can then factor out Cy and solve for it, which gives us Cy = 0.

Now, we can plug this value of Cy into our equation for Cx and solve for it, giving us Cx = 0.

Therefore, the vector C is C = 0i + 0j, which means it is a zero vector. This makes sense because a zero vector is perpendicular to all other vectors and has a dot product of 0 with any other vector.

In conclusion, the solution to this problem is a zero vector, C = 0i + 0j. I hope this helps guide you in your solution.