Question

Find the angle between vector a + vector b, vector a - vector b if vector a = i + 2j + k, vector b = 3i - j + 2k

Answer 1

vector a + vector b = (i + 2j + k) + (3i - j + 2k) = 4i + j + 3k

vector a - vector b = (i + 2j + k) - (3i - j + 2k) = -2i + 3j - k

cos(vector a + vector b, vector a - vector b) = (4i + j + 3k).(-2i + 3j - k)/ |4i + j + 3k||-2i +3j -k|

= -8+3-3/√16+√1+√9.√4+√9+√1

= -8/√364

= -8/2√91

= -4/√91

(vector a+ vector b, vector a- vector b) = cos-1(-4/√91)

= π - cos-1 (4/√91)