If A- B- C- are three non-coplanar vectors- then value of A-B-C-C-A-B-B-A-C-C-A-B-

The correct option is B 0Since A⃗,B⃗,C⃗ are non coplanar, we have [ A⃗B⃗C⃗ ]≠ 0 Also A⃗.B⃗×C⃗= [ A⃗B⃗C⃗ ], C⃗×A⃗.B⃗= [ C⃗A⃗B⃗ ]= [ A⃗B ...

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Condition for Two Lines to be on the Same Plane

If A⃗, B⃗, ...

Question

If $\to A, \to B, \to C$ are three non-coplanar vectors, then value of $\frac{\to A . \to B \times \to C}{\to C \times \to A . \to B} + \frac{\to B . \to A \times \to C}{\to C . \to A \times \to B}$

-1

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Solution

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[\to a \to b \to c] = 2

\frac{\to a . (\to b \times \to c)}{(\to c \times \to a) . \to b} + \frac{\to b . (\to c \times \to a)}{(\to a \times \to b) . \to c} + \frac{\to c . (\to a \times \to b)}{(\to b \times \to c) . \to a} =

If $\to a, \to b, \to c$ are three vectors such that $| \to a | = 5, | \to b | = 12$ and $| \to c | = 13$ and $\to a + \to b + \to c = 0$

Find the value of $\to a . \to b + \to b . \to c + \to c . \to a$ .

[\begin{matrix} \to a & \to b & \to c \end{matrix}] = 1

\frac{\to a . \to b \times \to c}{\to c \times \to a . \to b} + \frac{\to b . \to c \times \to a}{\to a \times \to b . \to c} + \frac{\to c . \to a \times \to b}{\to b \times \to c . \to a}

\to a, \to b, \to c

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

μ = \to a . \to b + \to b . \to c + \to c . \to a

| \to a | = 1; ∣ ∣ \to b ∣ ∣ = 4; | \to c | = 2

\to a, \to b, \to c

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

\to a . \to b + \to b . \to c + \to c . \to a

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