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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 14 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 14 Maths Textbook Solution.

Answers (1)

Answer: \vec{0}

Hint: You must know the rules of vector functions

Given: If D,E, F are the mid-points of sides BC,CA and AB respectively of \Delta ABC

            Write the value of \vec{AD}+\vec{BE}+\vec{CF}

Solution: D, E, F are the mid-points of sides BC, CA, AB respectively

            Then, the position vectors of the mid-points

             D, E, F are given by \frac{\vec{b}+\vec{c}}{2},\frac{\vec{c}+\vec{a}}{2},\frac{\vec{a}+\vec{b}}{2}

Now,

        \begin{aligned} &\overrightarrow{A D}+\overrightarrow{B E}+\overline{C F} \\ &\left(\frac{\vec{b}+\vec{c}}{2}\right)-\vec{a}+\left(\frac{\vec{c}+\vec{a}}{2}\right)-\vec{b}+\left(\frac{\vec{a}+\vec{b}}{2}\right)-\vec{c} \\ &2\left(\frac{\vec{a}+\vec{b}+\vec{c}}{2}\right)-(\vec{a}+\vec{b}+\vec{c}) \\ &\Rightarrow(\vec{a}+\vec{b}+\vec{c})-(\vec{a}+\vec{b}+\vec{c}) \\ &\Rightarrow \overrightarrow{0} \end{aligned}

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