Q. $\left\lbrack \mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ } \right\rbrack\mathbf{+}\left\lbrack \mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ } \right\rbrack\mathbf{+}\left\lbrack \mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ } \right\rbrack$ is equal to
Explanation
(d)
$\left\lbrack \mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ } \right\rbrack\mathbf{+}\left\lbrack \mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ } \right\rbrack\mathbf{+}\left\lbrack \mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ } \right\rbrack\mathbf{=}\left\lbrack \mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ } \right\rbrack\mathbf{+}\left\lbrack \mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ } \right\rbrack\mathbf{-}\left\lbrack \mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ } \right\rbrack$
$\mathbf{=}\left\lbrack \mathbf{\ }\widehat{\mathbf{i}}\mathbf{\ }\widehat{\mathbf{k}}\mathbf{\ }\widehat{\mathbf{j}}\mathbf{\ } \right\rbrack\mathbf{= \ }\widehat{\mathbf{i}}\mathbf{\bullet}\left( \widehat{\mathbf{k}}\mathbf{\times \ }\widehat{\mathbf{j}}\mathbf{\ } \right)$
$= \widehat{\mathbf{i}} \cdot \left( - \widehat{\mathbf{i}} \right) = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.