A) \[\overrightarrow{v}.(\overrightarrow{v}.\overrightarrow{a}t)={{\overrightarrow{v}}_{0}}({{\overrightarrow{v}}_{0}}+\overrightarrow{a}t)\]
B) \[\overrightarrow{v}.{{\overrightarrow{v}}_{0}}={{a}^{2}}{{t}^{2}}\]
C) \[\overrightarrow{v}.{{\overrightarrow{v}}_{0}}=\overrightarrow{a}.{{\overrightarrow{v}}_{0}}t\]
D) \[{{\overrightarrow{v}}_{0}}.{{\overrightarrow{v}}_{0}}=\overrightarrow{a}.{{\overrightarrow{v}}_{0}}\]
Correct Answer: A
Solution :
: We know that \[\overrightarrow{v}={{\overrightarrow{v}}_{0}}+\overrightarrow{a}t\] [a] L.H.S. \[=\overrightarrow{v}.(\overrightarrow{v}-\overrightarrow{a}\,t)\] \[=({{\overrightarrow{v}}_{0}}+\overrightarrow{a}\,t).{{\overrightarrow{v}}_{0}}={{\overrightarrow{v}}_{0}}.({{\overrightarrow{v}}_{0}}+\overrightarrow{a}\,t)\] \[=R.H.S.\]
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