If a = 2 i + j - k , b = i + 3 k and c is a unit vector, then the maximum value of the scalar triple product [ a b c ] is

Step-by-step solution

The scalar triple product is given by [ a b c ] = ( a b ) c . First, calculating the cross product a b : a b = vmatrix i & j & k 2 & 1 & -1 1 & 0 & 3 vmatrix = i (3 - 0) - j (6 - (-1)) + k (0 - 1) = 3 i - 7 j - k The scalar triple product becomes (3 i - 7 j - k ) c . Using the dot product formula, ( a b ) c = | a b | | c | , where is the angle between a b and c . Since c is a unit vector, | c | = 1 . The maximum value occurs when = 1 (i.e., when c is parallel to a b ). Maximum value = | a b | = 3^2 + (-7)^2 + (-1)^