(i) For any three vectors bar a, bar b, bar c show that bar a x (bar b + bar c) + bar b x (bar c x bar a) + bar c x (bar a + bar b) = 0

Question

(i) For any three vectors \(\bar a, \bar b, \bar c\), show that \(\bar a \times (\bar b + \bar c) + \bar b \times (\bar c + \bar a) + \bar c \times (\bar a +\bar b) \)=0

(ii) Given A (1, 1, 1), B (1, 2, 3), C (2, 3, 1) are the vertices of MBCa triangle. Find the area of the ∆ABC 

Answer 1

(i) \(\bar a \times (\bar b + \bar c) + \bar b \times (\bar c + \bar a) + \bar c \times (\bar a +\bar b) \)