10. vector algebra — ગણિત ધોરણ 12 સાયન્સ — Question

$=(\bar{a} \times \bar{b}) \cdot[(\vec{b} \times \vec{c}) \times(\vec{c} \times \vec{a})]$

$=(\vec{a} \times \vec{b}) \cdot[(\vec{b} \times \vec{c} \cdot \vec{a}) \vec{c}-(\vec{b} \times \vec{c} \cdot \vec{c}) \vec{a}]$

$ = (\vec a \times \vec b) \cdot [[\bar b\bar c\bar a]\vec c]\quad [\vec b \times \vec c.\vec c = 0]$

$=[\bar{a} \bar{b} \bar{c}] \cdot(\bar{a} \times \bar{b} \cdot \bar{c})=[\bar{a} \bar{b} \bar{c}]^{2}$

$[\vec{a} \times \vec{b} \vec{b} \times \vec{c} \quad \vec{c} \times \vec{a}]=[\bar{a} \bar{b} \bar{c}]^{2}$

So $\lambda=1$