A) \[\frac{1}{8}\]
B) \[\frac{25}{8}\]
C) 2
D) 5
Correct Answer: C
Solution :
\[\vec{a}=2\hat{i}+\hat{j}-2\hat{k},\,\vec{b}=\hat{i}+\hat{j}\]and \[|\vec{a}|=3\] \[\therefore \] \[\vec{a}\times \vec{b}=2\hat{i}-2\hat{j}+\hat{k}\] \[|\vec{a}\times \vec{b}|=3\] Now:\[(\vec{a}\times \vec{b})\times \vec{c}=|\vec{a}\times \vec{b}||\vec{c}|\sin 30\hat{n}\] \[|(\vec{a}\times \vec{b})\times \vec{c}|=3.|\vec{c}|.\frac{1}{2}\] \[3=3|\vec{c}|.\frac{1}{2}\] \[\therefore \] \[|\vec{c}|\,=2\] Now: \[|\vec{c}-\vec{a}|=3\] \[{{c}^{2}}+{{a}^{2}}-2\vec{c}.\vec{a}=9\] \[4+9-2\vec{a}.\vec{c}=9\] \[\vec{a}.\vec{c}=2\]
You need to login to perform this action.
You will be redirected in
3 sec
