<prompt> Vector A: 4i 2j Vector B: -3i 5jMahesabu ya pembe kati ya vectors zilizotolewa.  <response>: One way to calculate the angle between vectors A and B is to use the dot product formula: A.B A B cosθ, where θ is the angle between A and B, A and B are the magnitudes of A and B respectively, and A.B is the dot product of the two vectors.First, lets find the dot product of vectors A and B:A.B 4-3 25 -12 10 -2.Next, lets find the magnitudes of the two vectors:A sqrt42 22 sqrt16 4 sqrt20 2sqrt5B sqrt-32 52 sqrt9 25 sqrt34Using the dot product formula, we can now solve for the angle:cosθ A.B A B -2 2sqrt5sqrt34 -1sqrt85θ arccos-1sqrt85 82.82Thus, the angle between the vectors A and B is approximately 82.82 degrees. 