If be the angle between the vectors a=2 i +2 j - k and b=6 i -3 j +2 k , then

Step-by-step solution

The angle between two vectors a and b is given by the formula = a b | a | | b | . Given a = 2 i + 2 j - k and b = 6 i - 3 j + 2 k . Calculate the dot product a b = (2)(6) + (2)(-3) + (-1)(2) = 12 - 6 - 2 = 4 . Calculate the magnitude | a | = 2^2 + 2^2 + (-1)^2 = 4 + 4 + 1 = 9 = 3 . Calculate the magnitude | b | = 6^2 + (-3)^2 + 2^2 = 36 + 9 + 4 = 49 = 7 . Substitute these values into the formula: = 4 3 7 = 4 21 . Answer: = 4 21