Explanation

(a) $\overrightarrow{A} \times \overrightarrow{B} = \left( 4\widehat{i} + 6\widehat{j}\ \right) \times (2\widehat{i} + 3\widehat{j}\ )$
$= 12\left( \widehat{i} \times \widehat{j}\ \right) + 12\left( \widehat{j} \times \widehat{i}\ \right) = 12\left( \widehat{i} \times \widehat{j}\ \right) - 12\left( \widehat{i} \times \widehat{j}\ \right) = 0$
Again, $\overrightarrow{A} \bullet \overrightarrow{B} = \left( 4\widehat{i} + 6\widehat{j}\ \right) \bullet \left( 2\widehat{j} + 3\widehat{i}\ \right) = 8 + 18 = 26$
Again, $\frac{\left| \overrightarrow{A} \right|}{\left| \overrightarrow{B} \right|} = \frac{\sqrt{16 + 36}}{\sqrt{4 + 9}} \neq \frac{1}{2}$
Again , $\overrightarrow{B} = \frac{1}{2}\ \overrightarrow{A}$