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Collinear Vectors

1. If a , b ,...

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1. If a , b , c be three non coplanar vectors and r be any arbitrary vector , then (ab)(rc)+(bc)(ra)+(ca)(rb) is equal to

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\to a, \to b, \to c

be three non-coplanar vectors and

\to r

be any arbitrary vector, then

(\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)

¯ a

¯ b

¯ c

be three non-coplanar vectors and

{¯ a}_{1}

{¯ b}_{1}

{¯ c}_{1}

constitute the corresponding reciprocal system of vectors, then for any arbitrary vector

¯ r

.

\to a, \to b, \to c

be three non-coplanar vectors and

\to r

be any vector in space such that

\to r . \to a = 1, \to r . \to b = 2

\to r . \to c = 3.

[\to a, \to b, \to c] = 1

\to r

¯ a, ¯ b, ¯ c

are three non-coplanar, non-zero vectors and

¯ r

is any vector then

¯ r

can be represented as

x ¯ a + y ¯ b + z ¯ c

\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]

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Collinear Vectors

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