If a-b- c- are three non-zero- non-coplanar vectors and b-1-b-b-a-a-2a- b-2-b-b-a-a-2a- c-1-c-c-a-a-2a-b-c-c-2b-1- c-2-c-c-a-a-2a-b-1-c-b-1-2b-1- c-3-c-c-a-c-2a-b-c-c-2b-1- c-4-c-c-a-c-2a-b-c-b-2b-1- then the set of orthogonal vectors is

The correct option is C (a⃗,b⃗_1, c⃗_2) Pair of vectors (a⃗,b⃗) is orthogonal if their product is zero i.e. a⃗·b⃗ =0 Consider, a⃗·b⃗_1=(b⃗· ...

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Binomial Coefficients

If a⃗,b⃗, c...

Question

If $\to a, \to b, \to c$ are three non-zero, non-coplanar vectors and ${\to b}_{1} = \to b - \frac{\to b \cdot \to a}{| \to a |^{2}} \to a,$ ${\to b}_{2} = \to b + \frac{\to b \cdot \to a}{| \to a |^{2}} \to a$ , ${\to c}_{1} = \to c - \frac{\to c \cdot \to a}{| \to a |^{2}} \to a + \frac{\to b \cdot \to c}{| \to c |^{2}} {\to b}_{1},$ ${\to c}_{2} = \to c - \frac{\to c \cdot \to a}{| \to a |^{2}} \to a - \frac{{\to b}_{1} \cdot \to c}{| {\to b}_{1} |^{2}} {\to b}_{1},$ ${\to c}_{3} = \to c - \frac{\to c \cdot \to a}{| \to c |^{2}} \to a + \frac{\to b \cdot \to c}{| \to c |^{2}} {\to b}_{1}, {\to c}_{4} = \to c - \frac{\to c \cdot \to a}{| \to c |^{2}} \to a - \frac{\to b \cdot \to c}{| \to b |^{2}} {\to b}_{1}$ , then the set of orthogonal vectors is

(\to a, {\to b}_{1}, {\to c}_{3})

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(\to a, {\to b}_{1}, {\to c}_{2})

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(\to a, {\to b}_{1}, {\to c}_{1})

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(\to a, {\to b}_{2}, {\to c}_{2})

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\to a, \to b, \to c

\to a + \to b + \to c = \to 0

\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a =

\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, \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 .

\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 - 3 \to b + 4 \to c

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

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