<prompt> Bala angle pakeng tsa li-vector tse fanoeng.Vector A: 4i 2j Vector B: -3i 5j  <response>: Instruction in English: Calculate the angle between the given vectors. . Response in English: 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. . Response in Sesotho: Tsela e ngoe ea ho bala angle pakeng tsa li-vector A le B ke ho sebelisa foromo ea sehlahisoa sa matheba: AB A B cosθ, moo θ e leng angle pakeng tsa A le B, A le B ke boholo ba A le B ka ho latellana, me AB ke sehlahisoa sa matheba a li-vector tse peli. Pele, a re fumaneng sehlahisoa sa letheba la li-vectors A le B: AB 4 -3 2 5 -12 10 -2. Ka mora moo, a re fumaneng boholo ba li-vector tse peli: A sqrt42 22 sqrt16 4 sqrt20 2sqrt5 B sqrt-32 52 sqrt9 25 sqrt34 Re sebelisa foromo ea sehlahisoa sa letheba, joale re ka rarolla bakeng sa angle: cosθ AB A B -2 2sqrt5sqrt34 -1sqrt85 θ arccos-1sqrt85 82.82 Ka hona, angle pakeng tsa li-vector A le B e batla e le likhato tse 82,82. 