A) 6
B) 2
C) 20
D) 8
Correct Answer: C
Solution :
We have \[\vec{a}\times \vec{b}=4\] \[\Rightarrow \] \[|\overrightarrow{a}|\,\,.\,|\overrightarrow{b}|\sin \theta =4\] ... (1) \[\Rightarrow \] \[\sin \theta =\frac{4}{|\overrightarrow{a}|\,\,|\overrightarrow{b}|}\] Now \[|\overrightarrow{a}\,\,.\,\,\,\overrightarrow{b}|=2\] \[\Rightarrow \] \[|\overrightarrow{a}|\,.\,\,|\overrightarrow{b}{{|}^{2}}{{\cos }^{2}}\theta =4\] ... (2) or \[|\overrightarrow{a}{{|}^{2}}|\overrightarrow{b}|co{{s}^{2}}\theta =4\] \[\Rightarrow \] \[|\overrightarrow{a}{{|}^{2}}|\overrightarrow{b}{{|}^{2}}(1-{{\sin }^{2}}\theta )=4\] \[\Rightarrow \] \[|\overrightarrow{a}{{|}^{2}}|\overrightarrow{b}{{|}^{2}}\left( 1-\frac{16}{|\overrightarrow{a}{{|}^{2}}\,|\overrightarrow{b}{{|}^{2}}} \right)=4\] \[\Rightarrow \] \[|\overrightarrow{a}{{|}^{2}}\,|\overrightarrow{b}{{|}^{2}}-16=4\] \[|\overrightarrow{a}{{|}^{2}}=|\overrightarrow{b}{{|}^{2}}=20\]
You need to login to perform this action.
You will be redirected in
3 sec
