Find the linear relation between the following system of vectors a- b- c- being any three non-coplanar vectors- a-b-c- b-c-a- c-a-b- 2a-3b-4c-

The correct option is C ( 7/2 ) ( a b+c )+ ( b+c a ) 1/2 ( c+a+b )= 2a 3b+4c ...

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Applications of Dot Product

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Question

Find the linear relation between the following system of vectors $\to a, \to b, \to c$ being any three non-coplanar vectors:
$\to a - \to b + \to c, \to b + \to c - \to a, \to c + \to a + \to b, 2 \to a - 3 \to b + 4 \to c .$

(2) (a - b + c) + (3) (b + c - a) - \frac{1}{2} (c + a + b) = 2 a - 3 b + 4 c

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(3) (a - b + c) + (b + c - a) - (2) (c + a + b) = 2 a - 3 b + 4 c

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(7 / 2) (a - b + c) + (b + c - a) - \frac{1}{2} (c + a + b) = 2 a - 3 b + 4 c

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(5 / 2) (a - b + c) + (b + c - a) - \frac{1}{2} (c + a + b) = 2 a - 3 b + 4 c

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