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Question

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

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