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  • Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 3

Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 3

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Answer:-  0

Hint:- We use the section formula for finding coordinates of centroid.

Given:- If  \vec{a}, \vec{b}, \vec{c}   are the position vectors of the vectors of a triangle having its centroid at the origin then \vec{a}+\vec{b}+\vec{c}=\ldots .

Solution: Here the coordinates of D = (a+b)/2

 

                                                        

\begin{gathered} \frac{m \vec{b}+n \vec{a}}{m+n} \\\\ \frac{m}{n}=2 \end{gathered}

\begin{aligned} &\frac{2\left(\frac{\vec{a}+\vec{b}}{2}\right)+1(\vec{c})}{3} \\\\ &=G\left(\frac{\vec{a}+\vec{b}+\vec{c}}{3}\right) \end{aligned}

Here, given that centroid is at the origin (a + b + c)/3=0

Therefore, a+ b+ c =0

 

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