A) 88
B) 44
C) 22
D) none of these
Correct Answer: B
Solution :
Key Idea: \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}|\overrightarrow{b}{{|}^{2}}\] Given \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}=10,|\overrightarrow{a}|=3,|\overrightarrow{b}|=4\] \[\Rightarrow \] \[{{(10)}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}={{(3)}^{2}}.{{(4)}^{2}}\] \[\Rightarrow \] \[|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=9\times 16-100=144-100\] \[\Rightarrow \] \[|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=44\]
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