If a- b- and c- are three non-coplanar vectors- prove that -a- - b- - c- a- - b- a- - c- - -a- b- c-

Given a,b and c are three non coplanar vectorsTo prove: [a+b+c a+b a+c] = [a b c] Sol: [a+b+c a+b a+c] = (a+b+c). [(a+b) × (a+ ...

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Condition for Coplanarity of Four Points

If a⃗, b⃗ a...

Question

If $\to a, \to b$ and $\to c$ are three non-coplanar vectors, prove that
$[\to a + \to b + \to c \to a + \to b \to a + \to c] = - [\to a \to b \to c]$ .

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If $\to a, \to b$ and $\to c$ are three non-coplanar vectors, then $(\to a + \to b + \to c) \cdot [(\to a + \to b) \times (\to a + \to c)]$ equals

\to a, \to b, \to c

[\begin{matrix} \to a + \to b + \to c & \to a - \to c & \to a - \to b \end{matrix}]

If $\to a, \to b$ and $\to c$ are three non-coplanar vectors, then $(\to a + \to b + \to c) \cdot [(\to a + \to b) \times (\to a + \to c)]$ equals

\to a, \to b, \to c

\to a, \to b, \to c

\to a \times \to b = \to b \times \to c = \to c \times \to a

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

\to a, \to b, \to c

\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]}

(2 \to a + 3 \to b + 4 \to c) . \to p + (2 \to b + 3 \to c + 4 \to a) . \to q +

(2 \to c + 3 \to a + 4 \to b) . \to r =

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