Finding the Angle Between Two Vectors A & B

[vipertongn]

Homework Statement

Two vectors are given by A = -2 i + 5 j and B = 2 i + 3 j
Also find the angle between them

Homework Equations

Not really sure but from my book i get A x B = -B x A

The Attempt at a Solution

the answer is -16, but I'm confused I thought that it should look like -6 + 10 but why is it minus ten?

How would I use this to find the angle?

 

[Ofey]

Do you know how to set up a determinant for vector product? From the determinant you can easilly calculate the product vector. Remember the result of a vector product is always a vector.

When you know the vector product you can find the angle from

(AxB)=|A||B|sin(A,B)

Where A and B are the 2 vectors, (AxB) is the vector product and |A|/|B| are the lenghts of the vectors.

 

[nlightner]

I would suggest using the dot product formula to find the angle between two vectors A and B:

cosθ = (A•B) / (|A| * |B|)

Where A•B is the dot product of vectors A and B, and |A| and |B| are the magnitudes of vectors A and B, respectively.

In this case, the dot product of A and B is (-2*2) + (5*3) = -4 + 15 = 11. The magnitude of vector A is √((-2)^2 + (5)^2) = √(4+25) = √29. Similarly, the magnitude of vector B is √(2^2 + 3^2) = √(4+9) = √13.

Substituting these values into the formula, we get:

cosθ = (11) / (√29 * √13) = 11 / √377

Taking the inverse cosine of both sides, we get:

θ = cos^-1 (11 / √377) = 1.609 radians or 92.2 degrees (to the nearest tenth).

This means that the angle between vectors A and B is approximately 92.2 degrees.

As for the confusion about the answer being -16, it is possible that the student made a mistake in their calculations or misunderstood the question. The dot product should not result in a negative value, so -16 is not a correct answer in this case.