For three non coplanar vectors a- b- c- the relation - a-b-c- - - a- - - b- - - c- - holds if and only if

The correct option is B a⃗.b⃗=b⃗.c⃗=c⃗.a⃗=0 From given relation #160; | a⃗×b⃗·c⃗ |= | a⃗ | | b⃗ | | c⃗ | Let a⃗=î , #160; b⃗=ĵ and #16 ...

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Direction Cosines

For three non...

Question

For three non coplanar vectors $\to a, \to b, \to c$ the relation $∣ ∣ \to a \times \to b \cdot \to c ∣ ∣ = | \to a | ∣ ∣ \to b ∣ ∣ | \to c |$ holds if and only if

\to b . \to c = \to c . \to a = 0

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\to a . \to b = \to b . \to c = 0

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\to a . \to b = \to b . \to c = \to c . \to a = 0

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\to c . \to a = \to a . \to b = 0

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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} =

[\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

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

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

| \to a | = 1, ∣ ∣ \to b ∣ ∣ = 4 a n d | \to c | = 2

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