The angle between - ~ &~ - k is

Step-by-step solution

Let a = i - j and b = j - k . The dot product is given by a b = (1)(0) + (-1)(1) + (0)(-1) = -1 . The magnitudes are | a | = 1^2 + (-1)^2 + 0^2 = 2 and | b | = 0^2 + 1^2 + (-1)^2 = 2 . The cosine of the angle between the vectors is given by = a b | a | | b | . Substituting the values, = -1 2 2 = -1 2 . Since = - 1 2 , the angle = (- 1 2 ) = 2 3 . Answer: 2 3