If - a - b b - c c - a -1- a b c -then -1-2-3 is where a- b- c- are non zero and non coplanar vectors

[a+b b+c c+a]=(a+b).((b+c) × (c+a)) =(a+b).(b×c+b×a+c×a) =[abc]+[bca] =2[a b c] [a×b b×c c×a]=(a×b).((b×c) × (c×a)) =(a×b).[bca]c =[a ...

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Collinear Vectors

If [ a + b b...

Question

If $[\to a + \to b \to b + \to c \to c + \to a] = λ_{1} [\to a \to b \to c]$
and $[\to a \times \to b \to b \times \to c \to c \times \to a] = [\to a \to b \to c]^{λ_{2}}$
then $\frac{λ_{1} + λ_{2}}{3}$ is (where $\to a, \to b, \to c$ are non zero and non coplanar vectors)

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