A) \[\overrightarrow{\text{a}}\text{.(}\overrightarrow{\text{b}}\text{+}\overrightarrow{\text{c}}\text{)=}\overrightarrow{\text{b}}\text{.}\,\overrightarrow{\text{a}}\text{+}\overrightarrow{\text{a}}\text{.}\,\overrightarrow{\text{c}}\]
B) \[\overrightarrow{\text{a}}\text{ }\!\!\times\!\!\text{ (}\overrightarrow{\text{b}}\text{+}\overrightarrow{\text{c}}\text{)=}\,\text{(}\overrightarrow{\text{a}}\text{ }\!\!\times\!\!\text{ }\overrightarrow{\text{c}}\text{) }\!\!\times\!\!\text{ }\,\text{(}\overrightarrow{\text{a}}\text{ }\!\!\times\!\!\text{ }\overrightarrow{\text{b}}\text{)}\]
C) \[\overrightarrow{\text{a}}\text{ }\!\!\times\!\!\text{ (}\overrightarrow{\text{b}}\text{.}\overrightarrow{\text{c}}\text{)=}\,\text{(}\overrightarrow{\text{a}}\text{ }\!\!\times\!\!\text{ }\overrightarrow{\text{b}}\text{)}\text{.}\,\text{(}\overrightarrow{\text{a}}\text{ }\!\!\times\!\!\text{ }\overrightarrow{\text{c}}\text{)}\]
D) \[\text{(}\overrightarrow{\text{b}}\text{.}\overrightarrow{\text{c}}\text{)}\,\overrightarrow{\text{a}}\text{=}\overrightarrow{\text{a}}\,\text{(}\overrightarrow{\text{a}}\text{.}\overrightarrow{\text{b}}\text{)}\]
Correct Answer: A
Solution :
\[\overrightarrow{a}\]is a vector but \[(\overrightarrow{b}.\overrightarrow{c})\] is scalar quantity and the cross product between a vector and a scalar is undefined.
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