Let a-b-c- are three non-coplanar vectors such that r-1-a-b-c-r-2-b-c-a-r-3-c-a-b- r-2a-3b-4c- If r- 1r-1- 2r-2- 3r-3- then

The correct options are B λ _1+λ_3=3 C λ _1+λ_2+λ_3=4 r _ 1 = a b + c , r _ 2 = b + c a , r _ 3 = c + a + b , r =2 a 3 b ...

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Definite Integral as Limit of Sum

Let a⃗,b⃗,c...

Question

Let $\to a, \to b, \to c$ are three non-coplanar vectors such that $_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a,_{3} = \to c + \to a + \to b$ , $\to r = 2 \to a - 3 \to b + 4 \to c$ . If $\to r = λ_{1}_{1} + λ_{2}_{2} + λ_{3}_{3}$ then

λ_{1} = 7

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λ_{1} + λ_{3} = 3

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λ_{1} + λ_{2} + λ_{3} = 4

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λ_{3} + λ_{2} = 2

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Solution

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Similar questions

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a

_{3} = \to c + \to a + \to b, \to r = 2 \to a - 3 \to b + 4 \to c

\to r = λ_{1}_{1} + λ_{2}_{2} + λ_{3}_{3}

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a

_{3} = \to c + \to a - \to b, \to r = 2 \to a - 2 \to b + 4 \to c

\to r = x_{1}_{1} + x_{2}_{2} + x_{3}_{3}

\to a = 2^i + λ_{1}^j + 3^k

\to b = 4^i + (3 - λ_{2})^j + 6^k

\to c = 3^i + 6^j + (λ_{3} - 1)^k

\to b = 2 \to a

\to a

\to c

(λ_{1}, λ_{2}, λ_{3})

\to a, \to b, \to c

\to r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b) =

\to a, \to b, \to c

\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 .

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