If a, b, c are three non-coplanar vectors, then a b c c a b + b a… - Vidyadip

MCQ

If $\bar{a}, \bar{b}, \bar{c}$ are three non-coplanar vectors, then $\frac{\bar{a} \cdot \bar{b} \times \bar{c}}{\bar{c} \times \bar{a} \cdot \bar{b}}+\frac{\bar{b} \cdot \bar{a} \times \bar{c}}{\bar{c} \cdot \bar{a} \times \bar{b}}=$

✓
$0$
B
2
C
$-2$
D
None of these

✓

Answer

Correct option: A.

$0$

(A) $\frac{\bar{a} \cdot \bar{b} \times \bar{c}}{\bar{c} \times \bar{a} \cdot \bar{b}}+\frac{\bar{b} \cdot \bar{a} \times \bar{c}}{\bar{c} \cdot \bar{a} \times \bar{b}}=\frac{\bar{a} \cdot \bar{b} \times \bar{c}}{\bar{c} \cdot \bar{a} \times \bar{b}}+\frac{\bar{b} \cdot \bar{a} \times \bar{c}}{\bar{c} \cdot \bar{a} \times \bar{b}}$
$=\frac{[\overline{ a } \overline{ b } \overline{ c }]}{[\overline{ c } \overline{ a } \overline{ b }]}+\frac{[\overline{ b } \overline{ a } \overline{ c }]}{[\overline{ c } \overline{ a } \overline{ b }]}$
$=\frac{[\overline{ a } \overline{ b } \overline{ c }]}{[\overline{ c } \overline{ a } \overline{ b }]}-\frac{[\overline{ a } \overline{ b } \overline{ c }]}{[\overline{ c } \overline{ a } \overline{ b }]}=0$

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