If $\overrightarrow {\rm{a}}$ is any non-zero vector, then $(\overrightarrow {\rm{a}} \cdot \widehat {\rm{i}}) \cdot \widehat {\rm{i}} + (\overrightarrow {\rm{a}} \cdot \widehat {\rm{j}}) \cdot \widehat {\rm{j}} + (\overrightarrow {\rm{a}} \cdot \widehat {\rm{k}})\widehat {\rm{k}}$ is equal
to …………
Let $\overrightarrow {\rm{a}} = {a_1}\widehat {\rm{i}} + {a_2}\widehat {\rm{j}} + {a_3}\widehat {\rm{k}}$
$\therefore$ $\overrightarrow {\rm{a}} \cdot \widehat {\rm{i}} = {a_1},$ $\overrightarrow {\rm{a}} \cdot \widehat {\rm{j}} = {a_2}$
and $\overrightarrow {\rm{a}} \cdot \widehat {\rm{k}} = {a_3}$
$\therefore$ $(\overrightarrow {\rm{a}} \cdot \widehat {\rm{i}})\widehat {\rm{i}} + (\overrightarrow {\rm{a}} \cdot \widehat {\rm{j}})\widehat {\rm{j}} + (\overrightarrow {\rm{a}} \cdot \widehat {\rm{k}})\widehat {\rm{k}}$
$= {a_1}\widehat {\rm{i}} + {a_2}\widehat {\rm{j}} + {a_3}\widehat {\rm{k}} = \overrightarrow {\rm{a}}$
TRUE FALSE
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.