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Vectors and Its Types

If a, b, c ar...

Question

If a, b, c are three non-coplanar vectors such that $a + b + c = α d$ and $b + c + d = β a$ , then $a + b + c + d$ is equal to?

A

0

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B

α a

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C

β b

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D

(α + β) c

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Solution

The correct option is A $0$
$G i v e n, a + b + c = α d \Rightarrow b + c = α d - a - - - - - - (i) b + c + d = β a \Rightarrow b + c = β a - d - - - - - - (i i) c o m p a r e b o t h e q u (i) & (i i) α d - a = β a - d [\to d = \to a \Rightarrow (α + 1) d = (β + 1) a i f, α = - 1, β = - 1 t h e n, v a l u e i s 0 = 0, a n d, e q u^{n} a + b + c + d = o, i t m e a n s i f a + b + c + d i s e q u a l t o 0. s o t h a t w e c a n s a y t h e c o n d i t i o n i s c o r r e c t .$

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Similar questions

a, b, c

are three non-coplanar vectors such that

a + b + c = α d

b + c + d = β a

a + b + c + d

a + b + c = α d, b + c + d = β a

and a, b, c are non-coplanar vectors, then show the

a + b + c + d = 0

\to a, \to b, \to c

are non-coplanar and

\to a + \to b + \to c = α \to d

\to b + \to c + \to d = β \to a

\to a + \to b + \to c + \to d =

a + b + c = α d a n d b + c + d = β a

and a,b,c are non-coplanar vectors , then show that

a + b + c + d = 0

\vec{a,} \vec{b,} \vec{c}

are three non-coplanar vectors, such that

\vec{d} \cdot \vec{a} = \vec{d} \cdot \vec{b} = \vec{d} \cdot \vec{c} = 0,

\vec{d}

is the null vector.

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