If $\overrightarrow{\mathbf{a}} \bullet \widehat{\dot{\mathbf{i}}} = 4$ then $\left( \overrightarrow{\mathbf{a}} imes \widehat{\dot{\mathbf{j}}} ight) \bullet (2\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}})$ is equal to

Question

If $\overrightarrow{\mathbf{a}} \bullet \widehat{\dot{\mathbf{i}}} = 4$ then $\left( \overrightarrow{\mathbf{a}} 	imes \widehat{\dot{\mathbf{j}}} ight) \bullet (2\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}})$ is equal to

Dr. Abubacker · Accepted Answer

(d)
$\left( \overrightarrow{\mathbf{a}} 	imes \widehat{\dot{\mathbf{j}}} ight) \bullet \left( 2\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}} ight) = \overrightarrow{\mathbf{a}} \bullet \left\{ \widehat{\dot{\mathbf{j}}} 	imes \left( 2\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}} ight) ight\}$
$= \overrightarrow{\mathbf{a}} \bullet \left\{ - 3\left( \widehat{\dot{\mathbf{j}}} 	imes \widehat{\mathbf{k}} ight) ight\} = - 3\left( \overrightarrow{\mathbf{a}} \bullet \widehat{\dot{\mathbf{i}}} ight)$
$= - 12$ $\lbrack\because\overrightarrow{\mathbf{a}} \bullet \widehat{\dot{\mathbf{i}}} = 4,$ given]

Q. If $\overrightarrow{\mathbf{a}} \bullet \widehat{\dot{\mathbf{i}}} = 4$ then $\left( \overrightarrow{\mathbf{a}} \times \widehat{\dot{\mathbf{j}}} \right) \bullet (2\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}})$ is equal to

Explanation

Reviewed by Dr. Abubacker

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