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.

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

thanks

To find the components of vector C, we can use the fact that vector C is perpendicular to vector A. Since two vectors are perpendicular if their dot product is zero, we can set up the dot product of vector C and vector A equal to zero and solve for the components of vector C.

The dot product of two vectors can be found by multiplying their corresponding components and summing the results. So, for vectors A and C, the dot product can be expressed as:

A · C = (5.0i - 6.5j) · (Cx i + Cy j) = 0

Expanding this equation, we get:

5.0Cx - 6.5Cy = 0

Now, we are given that the scalar product of vector C with vector B is 15, and the scalar product is also calculated by taking the dot product of the two vectors:

B · C = (-3.5i + 7.0j) · (Cx i + Cy j) = 15.0

Expanding this equation, we get:

-3.5Cx + 7.0Cy = 15.0

We now have a system of two linear equations with two unknowns. We can solve these equations simultaneously to find the components of vector C.

Using the method of substitution or elimination, we can solve the above equations to find the values of Cx and Cy.

Solving these equations, we find:
Cx = 26/13 ≈ 2.0
Cy = 20/13 ≈ 1.54

Therefore, the components of vector C are approximately Cx = 2.0 and Cy = 1.54.

you're welcome!

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.