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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 22

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 22

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Answer: \frac{\sqrt{35}}{2}

Hint: The length of median by median formula

Given: The vector 2 \hat{j}+\hat{k} \& 3 \hat{i}-\hat{j}+4 \hat{k}  represent two side \mathrm{AB}\; \&\; \mathrm{AC} \text { of } \Delta A B C. Find length of median,

Solution:

                \begin{aligned} &\overrightarrow{B C}=\overrightarrow{A C}-\overrightarrow{A B} \\\\ &=(3 \hat{i}-\hat{j}+4 \hat{k})-(2 \hat{j}+\hat{k}) \\\\ &=3 \hat{i}-3 \hat{j}+3 \hat{k} \end{aligned}

                \begin{aligned} &\overrightarrow{B D}=\frac{1}{2} B C \Rightarrow \frac{3}{2} \hat{i}-\frac{3}{2} \hat{j}+\frac{3}{2} \hat{k} \\\\ &\overrightarrow{A D}=A B+B D \\\\ &=(2 \hat{j}+\hat{k})+\left(\frac{3}{2} \hat{i}-\frac{3}{2} \hat{j}+\frac{3}{2} \hat{k}\right) \end{aligned}

                \begin{gathered} \overrightarrow{A D}=\frac{3}{2} \hat{\imath}+\frac{1}{2} \hat{\jmath}+\frac{5}{2} \hat{k} \\\\ |A D|=\sqrt{\left(\frac{3}{2}\right)^{2}+\left(\frac{1}{2}\right)^{2}+\left(\frac{5}{2}\right)^{2}} \end{gathered}

                =\sqrt{\frac{9}{4}+\frac{1}{4}+\frac{25}{4}}=\sqrt{\frac{35}{4}}=\frac{\sqrt{35}}{2}

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