For any three vectors a - - b - - c - the expression a - b - b - c - C - a - equalsa a - b - c -b 2 a - b - c -c a - b - c - 2d none of these

(d) none of these nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; We #160;have #160;a #8594; b #8594;.b #8594; c #8594; #215;c #8594; a #8594 ...

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Selecting Consecutive Terms in A.P

For any three...

Question

For any three vectors $\vec{a,} \vec{b,} \vec{c}$ the expression $(\vec{a} - \vec{b}) . \{(\vec{b} - \vec{c}) \times (\vec{c} - \vec{a})\}$ equals
(a) $[\vec{a} \vec{b} \vec{c}]$

(b) $2 [\vec{a} \vec{b} \vec{c}]$

(c) ${[\vec{a} \vec{b} \vec{c}]}^{2}$

(d) none of these

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\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}]

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

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

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

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

[a + b, b + c, c + a]

[b + c c + a a + b] = 2 [a b c]

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