Find the angle (in degrees) between vectors <1,3> and <2,-5>.

To find the angle between two vectors, we can use the formula for the dot product of two vectors, which is given by:

A · B = ||A|| ||B|| cos θ

where:

• A · B is the dot product of A and B,
• ||A|| is the magnitude of A,
• ||B|| is the magnitude of B, and
• θ is the angle between A and B.

Given the vectors A = <1,3> and B = <2,-5>, we can calculate the dot product as follows:

A · B = (12) + (3-5) = 2 - 15 = -13

Next, we calculate the magnitudes of A and B:

||A|| = sqrt((1^2) + (3^2)) = sqrt(1 + 9) = sqrt(10) ||B|| = sqrt((2^2) + (-5^2)) = sqrt(4 + 25) = sqrt(29)

Substituting these values into the formula, we get:

-13 = sqrt(10) * sqrt(29) * cos θ

Solving for cos θ, we get:

cos θ = -13 / (sqrt(10) * sqrt(29))

Finally, we can find the angle θ by taking the inverse cosine (or arccos) of the above value. Remember to convert the result from radians to degrees by multiplying by 180/π.

θ = arccos(-13 / (sqrt(10) * sqrt(29))) * (180/π)

This will give you the angle in degrees between the two vectors.