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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 27

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 27

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Answer:\sqrt{209}

Hint: |\vec{a}+\vec{b}+\vec{c}|

Given: If  \vec{a}, \vec{b}, \vec{c}  are position vectors of point A(2,3,-4), B(3,-4,-5) \; \& \; C(3,2,-3)

Then |\vec{a}+\vec{b}+\vec{c}| is equal to

Solution:

            \begin{aligned} &\vec{a}=2 \hat{i}+3 \hat{j}-4 \hat{k} \\\\ &\vec{b}=3 \hat{i}-4 \hat{j}-5 \hat{k} \\\\ &\vec{c}=3 \hat{i}+2 \hat{j}-3 \hat{k} \end{aligned}

            \begin{gathered} |\vec{a}+\vec{b}+\vec{c}|=(2+3+3) \hat{i}+(3-4+2) \hat{j}+(-4-5-3) \hat{k} \\\\ \end{gathered}

                                =8 \hat{i}+\hat{j}-12 \hat{k}

            Magnitude:

                            \begin{aligned} &=\sqrt{8^{2}+1^{2}+(-12)^{2}} \\\\ &=\sqrt{64+1+144} \\\\ &=\sqrt{209} \end{aligned}

 

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