Question

$\mathrm{What}\mathrm{will}\mathrm{be}\mathrm{the}\mathrm{magnitude}\mathrm{of}\mathrm{the}\mathrm{vector}\overrightarrow{V},\mathrm{which}\mathrm{is}\mathrm{the}\mathrm{sum}\mathrm{of}3\mathrm{times}\mathrm{the}\mathrm{vector}\overrightarrow{A}=2\hat{i}+2\hat{j}-6\hat{k}\mathrm{and}-2\mathrm{times}\mathrm{the}\mathrm{vector}\overrightarrow{B}=6\hat{i}-3\hat{j}-11\hat{k}$

• A. $14$
• B. $18$
• C. $12$
• D. $16$

Answer 1

The correct option is A $14$

$\mathrm{According}\mathrm{to}\mathrm{the}\mathrm{given}\mathrm{condition}-\overrightarrow{V}=3\overrightarrow{A}-2\overrightarrow{B}\mathrm{So},3\overrightarrow{A}=3(2\hat{i}+2\hat{j}-6\hat{k})=6\hat{i}+6\hat{j}-18\hat{k}\mathrm{and}-2\overrightarrow{B}=-2(6\hat{i}-3j-11\hat{k})=-12\hat{i}+6j+22\hat{k}\Rightarrow \overrightarrow{V}=\left(6-12\right)\hat{i}+\left(6+6\right)\hat{j}+\left(-18+22\right)\hat{k}\Rightarrow \overrightarrow{V}=-6\hat{i}+12\hat{j}+4\hat{k}\left(\overrightarrow{V}\right|=\sqrt{{\left(-6\right)}^2+{\left(12\right)}^2+{\left(4\right)}^2}\Rightarrow \left(\overrightarrow{V}\right|=14$