QJEEM20Ma9967: JEE Main 2020 Physics - Class 11 JEEM20Ma9967 Solution: Let , and be three vectors such that , and the angle between…

Given $\left| {\overrightarrow a } \right| = \sqrt 3$ , $\left| {\overrightarrow b } \right| = 5$

Given $\overrightarrow b .\overrightarrow c = 10$

And the angle between $\overrightarrow b$ and $\overrightarrow c$ is ${\pi \over 3}$

$\therefore$ $bc\cos {\pi \over 3}$ = 10

$\Rightarrow$ c = 4

${\overrightarrow a }$ is perpendicular to the vector $\overrightarrow b \times \overrightarrow c$

$\therefore$ $\overrightarrow a .\left( {\overrightarrow b \times \overrightarrow c } \right)$ = 0 and angle between them is ${\pi \over 2}$

Now $\left| {\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right)} \right|$

= $\left| {\overrightarrow a } \right|\left| {\overrightarrow b \times \overrightarrow c } \right|\sin {\pi \over 2}$

= $\left| {\overrightarrow a } \right|$ . ${\left| {\overrightarrow b } \right|.\left| {\overrightarrow c } \right|}$ $\sin {\pi \over 3}$ .1

= $\sqrt 3 \times 5 \times 4 \times {{\sqrt 3 } \over 2}$

= 30