Q. If unit vector$\ \overrightarrow{\mathbf{c}}$ makes an angle $\frac{\pi}{3}$ with $\widehat{\mathbf{i}}\mathbf{+}\widehat{\mathbf{j}}$, then minimum and maximum values of $(\widehat{\mathbf{i}}\mathbf{\times}\widehat{\mathbf{j}}\mathbf{\ }) \bullet \overrightarrow{\mathbf{c}}$ respectively are
A) $0,\ \frac{\sqrt{3}}{2}$
B) $- \frac{\sqrt{3}}{2},\ \frac{\sqrt{3}}{2}$
C) $- 1,\ \frac{\sqrt{3}}{2}$
D) None of these
Explanation
(b)
$(\widehat{\mathbf{i}}\mathbf{\times}\widehat{\mathbf{j}}\mathbf{\ )}\mathbf{\bullet}\overrightarrow{\mathbf{c}} \leq |\widehat{\mathbf{i}}\mathbf{\times}\widehat{\mathbf{j}}|\left| \overrightarrow{c}\ \right|\cos\frac{\pi}{6}$
$\Rightarrow \ - \frac{\sqrt{3}}{2} \leq (\widehat{\mathbf{i}}\mathbf{\times}\widehat{\mathbf{j}}\mathbf{\ ) \bullet}\overrightarrow{\mathbf{c}} \leq \frac{\sqrt{3}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.