A) \[\sqrt{7}\]
B) \[\frac{7}{\sqrt{2}}\]
C) \[\frac{\sqrt{7}}{2}\]
D) \[\frac{49}{18}\]
Correct Answer: D
Solution :
\[\left( \sqrt{2}a\hat{i}+b\hat{j}+c\hat{k} \right).\left( 2\sqrt{2}\hat{i}+3\hat{j}+\hat{k} \right)\] \[=\sqrt{2{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\sqrt{18}\cos \theta .\] \[{{\left( \sqrt{2{{a}^{2}}+{{b}^{2}}+{{c}^{2}}} \right)}_{\min .}}=\frac{7}{3\sqrt{2}};\] when\[\cos \theta =1\]. \[\therefore \]\[{{(2{{a}^{2}}+{{b}^{2}}+{{c}^{2}})}_{\min .}}=\frac{49}{18}.\]
You need to login to perform this action.
You will be redirected in
3 sec
