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Vector Addition

if a,b,c are ...

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if a,b,c are non coplanar vectors ,nonzero vectors ,the the value of (\overrightarrow a\cdot\overrightarrow a)\overrightarrow b×\overrightarrow c+(\overrightarrow a\cdot\overrightarrow b)\overrightarrow c×\overrightarrow a+(\overrightarrow a\cdot\overrightarrow c)\overrightarrow a×\overrightarrow{b is

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\to a =^i +^j +^k, \to b

\to c =^j -^k

be three vectors such that

\to a \times \to b = \to c

\to a \cdot \to b = 1

. If the length of projection vector of the vector

\to b

\to a \times \to c

l

, then the value of

3 l^{2}

\to a, \to b, \to c

are non coplanar vectors, then

[\to a \times \to b, \to b \times \to c, \to c \times \to a]

\to a, \to b, \to c

are non coplanar vectors such that

\to b \times \to c = \to a, \to a \times \to b = \to c

\to c \times \to a = \to b

\to a, \to b, \to c

be any three non - coplanar vectors, then calculate the value of

[\to a + \to b \to b + \to c \to c + \to a]

\to a, \to b, \to c

are non coplanar vectors and

λ

is a real number, then the vectors

\to a + 2 \to b + 3 \to c, λ \to b + 4 \to c

(2 λ - 1) \to c

are non coplanar for:

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