 Hello and welcome to the session. The given question says find the angle between the vectors A vector plus B vector and vector A minus vector B. If vector A is equal to 2i cap minus j cap plus 3k cap and vector B is equal to 3i cap plus j cap minus 2k cap. Let's start with the solution and here we are given 2 vectors A and B and vector A is equal to 2i cap minus j cap plus 3k cap and vector B is equal to 3i cap plus j cap minus 2k cap. First let us find the sum of both these vectors that is vector A plus vector B. This is equal to 5i cap plus 0j cap plus 1k cap and now let us find the difference that is A vector minus B vector. So this gives minus i cap minus 2j cap plus 5k cap. Let us denote the sum of both these vectors by vector x and A vector minus B vector as vector y. Now first let us learn that the angle between two vectors x and y is given by cos theta is equal to dot product of vectors x and y divided by the product of their magnitudes or theta is equal to cos inverse of dot product of vectors x and y divided by the product of their magnitudes. So here first let us find the dot product of vectors x and y. So this is equal to 5 into minus 1 plus 0 into minus 2 plus 1 into 5 that is multiplying the coefficients of i cap, j cap and k cap and then adding the sketch minus 5 plus 0 plus 5 which is equal to 0. Now let us find the magnitude of vector x it is equal to root over 5 square plus 0 square plus 1 square. So this is equal to root over 25 plus 1 which is equal to root over 26 and now let us find the magnitude of vector y this is equal to 1 square minus 1 square gives 1 square plus minus of 2 whole square plus 5 square and this is equal to root over 1 plus 4 plus 25 which is equal to root over 30 and thus cos theta is equal to dot product of vectors x and y divided by their magnitudes. So this is equal to 0 divided by root over 26 into root over 30 which is equal to 0. Therefore we have cos theta is equal to 0 or theta is equal to cos inverse 0 and cos is 0 at pi by 2 so theta is equal to pi by 2. Therefore angle between the vectors x and y or vector a plus vector b and vector a minus vector b is pi by 2 that is both the vectors are perpendicular to each other. So this completes the session by