A) 12
B) 3
C) 8
D) 4
Correct Answer: B
Solution :
Key Idea: \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{b}.\overrightarrow{b}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}|\overrightarrow{b}{{|}^{2}}\] Given \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=144\] and \[|\overrightarrow{a}|=4\] \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=|\vec{a}{{|}^{2}}|\overrightarrow{b}{{|}^{2}}\] \[\Rightarrow \] \[144=16.|\overrightarrow{b}{{|}^{2}}\] \[\Rightarrow \] \[|\overrightarrow{b}{{|}^{2}}=9\] \[\Rightarrow \] \[|\overrightarrow{b}|=3\]You need to login to perform this action.
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