Question

# If $$a, b, c$$ are three non-coplanar vectors such that $$a + b + c = \alpha d$$ and $$b + c + d = \beta a$$ then $$a+ b+ c+d$$ is equal to

A
0
B
αa
C
βb
D
(α+β)c

Solution

## The correct option is A $$0$$$$a + b + c =\alpha (\beta a -b -c)$$$$\Rightarrow (1-\alpha\beta )a+(1+\alpha )b+(1+\alpha )c=0$$$$\Rightarrow 1 =\alpha \beta$$ and $$\alpha = -1 (a, b, c$$ are non-coplanar so linearly independent)Substitute the value $$\alpha =-1,$$ we get $$a + b + c + d=0$$Mathematics

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