Two vectors are described by the following equations, where i and j are unit vectors in the x- and y-directions:a = 2i + jb = i + 3jWhat is the angle between these two vectors? Give your answer in degrees (round to whole integer).

The angle between two vectors can be found using the dot product formula:

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
• θ is the angle between a and b

First, let's find the dot product of a and b:

a · b = (2i + j) · (i + 3j) = 21 + 13 = 2 + 3 = 5

Next, let's find the magnitudes of a and b:

||a|| = sqrt((2)^2 + (1)^2) = sqrt(4 + 1) = sqrt(5) ||b|| = sqrt((1)^2 + (3)^2) = sqrt(1 + 9) = sqrt(10)

Now, we can substitute these values into the dot product formula and solve for θ:

5 = sqrt(5) * sqrt(10) * cos θ cos θ = 5 / (sqrt(5) * sqrt(10)) cos θ = 5 / sqrt(50) cos θ = 5 / (5*sqrt(2)) cos θ = 1 / sqrt(2)

Finally, we can find the angle θ by taking the inverse cosine (cos^-1) of 1 / sqrt(2):

θ = cos^-1(1 / sqrt(2))

Converting this to degrees (since the inverse cosine function typically gives an answer in radians), we get:

θ = 45 degrees

So, the angle between the two vectors a and b is approximately 45 degrees.