If a - b - c - are non-coplanar vectors- then b - C - a -b -c - a - b - c -

For #160;non #8208;coplanar #160;vectors #160;a #8594;, #160;b #8594; #160;and #160;c #8594;b #8594; #215;c #8594; #183;a #8594;+b ...

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Addition of Vectors

If a →, b →, ...

Question

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors, then $\frac{(\vec{b} \times \vec{c}), (\vec{a} + \vec{b} + \vec{c})}{[\vec{a} \vec{b} \vec{c}]}$ = _______________.

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\vec{a,} \vec{b,} \vec{c}

\frac{\vec{a} \cdot (\vec{b} \times \vec{c})}{(\vec{c} \times \vec{a}) \cdot \vec{b}} + \frac{\vec{b} \cdot (\vec{a} \times \vec{c})}{\vec{c} \cdot (\vec{a} \times \vec{b})}

\vec{a,} \vec{b,} \vec{c}

(\vec{a} + \vec{b} + \vec{c}) . [(\vec{a} + \vec{b}) \times (\vec{a} + \vec{c})]

[\vec{a} \vec{b} \vec{c}]

2 [\vec{a} \vec{b} \vec{c}]

- [\vec{a} \vec{b} \vec{c}]

a, b, c

(a . a) b \times c + (a . b) c \times a + (a . c) a \times b = [b c a] a

a, b, c

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

\to a, \to b, \to c

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

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

\to a, \to b, \to c

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

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

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