Given $\left| {{\vec A_1}} \right| = 2,\,\left| {{\vec A_2}} \right| = 3$ and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 3$. Find the value or $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} - 4{{\vec A}_2}} \right)} \right|$
Given $\left| {{\vec A_1}} \right| = 2,\,\left| {{\vec A_2}} \right| = 3$ and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 3$. Find the value or $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} - 4{{\vec A}_2}} \right)} \right|$
- A
$64$
- B
$60$
- C
$62$
- D
$61$
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If $\theta$ is the angle between two vectors $A$ and $B$, then match the following two columns.
colum $I$
colum $II$
$(A)$ $A \cdot B =| A \times B |$
$(p)$ $\theta=90^{\circ}$
$(B)$ $A \cdot B = B ^2$
$(q)$ $\theta=0^{\circ}$ or $180^{\circ}$
$(C)$ $|A+B|=|A-B|$
$(r)$ $A=B$
$(D)$ $|A \times B|=A B$
$(s)$ None
| colum $I$ | colum $II$ |
| $(A)$ $A \cdot B =| A \times B |$ | $(p)$ $\theta=90^{\circ}$ |
| $(B)$ $A \cdot B = B ^2$ | $(q)$ $\theta=0^{\circ}$ or $180^{\circ}$ |
| $(C)$ $|A+B|=|A-B|$ | $(r)$ $A=B$ |
| $(D)$ $|A \times B|=A B$ | $(s)$ None |