उत्तर (2)

समाधान

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

$\vec{a} \cdot(\vec{c} \times \vec{b})-\vec{a} \cdot \vec{b}-\vec{a} \cdot \vec{c} ~ \ldots (i)$

दिया गया है $\overrightarrow{a} \times \overrightarrow{c}=\overrightarrow{b}$

$\Rightarrow(\overrightarrow{a} \times \overrightarrow{c}) \cdot \overrightarrow{b}=\overrightarrow{b} \cdot \overrightarrow{b}=|\overrightarrow{b}|^{2}=27 $

$\Rightarrow \vec{a} \cdot(\vec{c} \times \vec{b})=\left[\begin{array}{lll}\vec{a} & \vec{c} & \vec{b}\end{array}\right]=(\vec{a} \times \vec{c}) \cdot \vec{b}=27 ~\ldots (ii)$

अब $\vec{a} \cdot \vec{b}=3-6+3=0 ~ \ldots (iii) $

$\overrightarrow{a} \cdot \overrightarrow{c}=3$…(iv) (दिया गया)

(i), (ii), (iii) और (iv) से:

$=27-0-3=24$