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Vectors and Scalar

39. if the th...

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39. if the three vectors a, b, c are non-coplanar. express a, b, c each in terms of the vectors bc, ca, ab.

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\to a, \to b, \to c

are non collinear coplanar vectors represents

- - \to B C, - - \to C A, - - \to A B

respectively, then which of the following is TRUE

Q. Assertion :If

a, b, c

are three non-coplanar, non-zero vectors, then

(a . a) b \times c + (a . b) c \times a + (a . c) a \times b = [b c a] a

Reason: If the vectors

a, b, c

are non-coplanar, then so are

b \times c, c \times a, a \times b

\to a, \to b, \to c

are three non-coplanar vectors,

\to p, \to q, \to r

are non-zero vectors such that

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]},

then the value of the expression

(\to a + \to b + \to c), (\to p + \to q + \to r)

A, B

c

are three non-coplanar vectors, then

(A + B + C) . [(A + B) \times (A + C)]

a, b, c

are three non-coplanar vectors, then

(a + b + c) \cdot ((a + b) \times (a + c))

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