Question

If ${\bf{\vec a}},{\bf{\vec b}},{\bf{\vec c}}$ are three non-zero, non-coplanar vectors and ${{{\bf{\vec b}}}_1} + {\bf{\vec b}} - \frac{{{\bf{\vec b}}\cdot{\bf{\vec a}}}}{{|{\bf{\vec a}}{|^2}}}{\bf{\vec a}}\;\;\;\;\;\;\;,{{{\bf{\vec b}}}_2} + {\bf{\vec b}} - \frac{{{\bf{\vec b}}\cdot{\bf{\vec a}}}}{{|{\bf{\vec a}}{|^2}}}{\bf{\vec a}}\;\;\;$ And ${\rm{\;}}{{{\bf{\vec c}}}_1} + {\bf{\vec b}} - \frac{{{\bf{\vec c}}\cdot{\bf{\vec a}}}}{{|{\bf{\vec a}}{|^2}}}{\bf{\vec a}} + \frac{{{\bf{\vec c}}\cdot{\bf{\vec b}}}}{{|{\bf{\vec b}}{|^2}}}{{{\bf{\vec b}}}_1}\;$ ${{{\bf{\vec c}}}_2} + {\bf{\vec c}} - \frac{{{\bf{\vec c}}\cdot{\bf{\vec a}}}}{{|{\bf{\vec a}}{|^2}}}{\bf{\vec a}} - \frac{{{\bf{\vec c}}\cdot{{{\bf{\vec b}}}_1}}}{{|{{{\bf{\vec b}}}_1}{|^2}}}{{{\bf{\vec b}}}_1}\;,\;\;\;$ ${{{\bf{\vec c}}}_3} = {\bf{\vec c}} - \frac{{{\bf{\vec c}}\cdot{\bf{\vec a}}}}{{|{\bf{\vec c}}{|^2}}}{\bf{\vec a}} - \frac{{{\bf{\vec c}}\cdot{{{\bf{\vec b}}}_2}}}{{|{\bf{\vec c}}{|^2}}}{{{\bf{\vec b}}}_1},\;$ ${{{\bf{\vec c}}}_4} = {\bf{\vec c}} - \frac{{{\bf{\vec c}}\cdot{\bf{\vec a}}}}{{|{\bf{\vec c}}{|^2}}}{\bf{\vec a}} - \frac{{{\bf{\vec b}}\cdot{\bf{\vec c}}}}{{|{\bf{\vec b}}{|^2}}}{{{\bf{\vec b}}}_1}$ Then, which of the following is a set of mutually orthogonal vectors?

Accepted Answer

$\left\{ {{\bf{\vec a}},\;{{{\bf{\vec b}}}_1},{{{\bf{\vec c}}}_2}} \right\}$

Answer

$\left\{ {{\bf{\vec a}},\;{{{\bf{\vec b}}}_1},{{{\bf{\vec c}}}_1}} \right\}\;$

Answer

$\left\{ {{\bf{\vec a}},\;{{{\bf{\vec b}}}_2},{{{\bf{\vec c}}}_3}} \right\}$

Answer

$\left\{ {{\bf{\vec a}},\;{{{\bf{\vec b}}}_2},{{{\bf{\vec c}}}_4}} \right\}$

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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