Find the angle 𝜃 (in radians) between the vectors. (Round your answer to two decimal places.)u  =  4i − 5jv  =  i − 5j

The angle θ between two vectors u and v can be found using the dot product formula:

u . v = ||u|| ||v|| cos(θ)

where:

• u . v is the dot product of u and v
• ||u|| is the magnitude of vector u
• ||v|| is the magnitude of vector v

First, calculate the dot product of u and v:

u . v = (4i - 5j) . (i - 5j) = 41 + (-5)(-5) = 4 + 25 = 29

Next, calculate the magnitudes of u and v:

||u|| = sqrt((4)^2 + (-5)^2) = sqrt(16 + 25) = sqrt(41) ||v|| = sqrt((1)^2 + (-5)^2) = sqrt(1 + 25) = sqrt(26)

Then, substitute these values into the dot product formula and solve for θ:

cos(θ) = (u . v) / (||u|| ||v||) = 29 / (sqrt(41) * sqrt(26))

θ = arccos(29 / (sqrt(41) * sqrt(26)))

Finally, use a calculator to find the arccos of the value. Make sure your calculator is set to radians. Round your answer to two decimal places.