If a-b-c and p-q-r are two sets of three non-coplanar vectors such that a-p-b-q-c-r-3 then value of p- q and r is

The correct option is D b × c [ a b c ] , c × a [ a b c ] , a × b [ a b c ] We have #160; a.p+b.q+c.r=3 Multiply and Divide RHS by ...

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Unit Vectors

If a,b,c an...

Question

If $\to a, \to b, \to c$ and $\to p, \to q, \to r$ are two sets of three non-coplanar vectors such that $\to a . \to p + \to b . \to q + \to c . \to r = 3$ then value of $\to p$ , $\to q$ and $\to r$ is

\frac{\to a \times \to b}{[\to a \to b \to c]}, \frac{\to b \times \to c}{[\to a \to b \to c]}, \frac{\to c \times \to a}{[\to a \to b \to c]}

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

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\frac{\to a}{{∣ ∣ \to a ∣ ∣}^{2}}, \frac{\to b}{{∣ ∣ ∣ \to b ∣ ∣ ∣}^{2}}, \frac{\to c}{{∣ ∣ \to c ∣ ∣}^{2}}

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\frac{\to b \times \to c}{[\to a \to b \to c]}, \frac{\to c \times \to a}{[\to a \to b \to c]}, \frac{\to a \times \to b}{[\to a \to b \to c]}

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\to a, \to b, \to c

\to p, \to q, \to r

\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]},

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

\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]}

\to a, \to b

\to c

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

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

a, b, c

(a + b + c) . (p + q + r)

\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]}

\to a, \to b

\to c

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

\to a, \to b, \to c

\to p = \frac{\to b \times \to a}{[\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]}

(\to a + \to b) . \to p + (\to b + \to c) . \to q + (\to c + \to a) . \to r =

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