If scalar triple product of vectors ^i+^j+^k,3^i+4^j+5^k,7^i+2^j+11^k is given by the determinant ∣∣
∣∣a1a2a3b1b2b3c1c2c3∣∣
∣∣ then a1+b2+c3=__.
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Solution
Let’s say we have 3 vectors a1^i+a2^j+a3^k b1^i+b2^j+b3^k c1^i+c2^j+c3^k Then their scalar triple product is given by following determinant ∣∣
∣∣a1a2a3b1b2b3c1c2c3∣∣
∣∣ So a1 = Coefficient of ^i in first vector =1 b2 = Coefficient of ^j in second vector = 4 c3 = Coefficient of ^k in third vector =11 So a1+b2+c3=11+4+1=16