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  • Provide Solution For R. D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 13 Maths Textbook Solution.

Provide Solution For  R. D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 13 Maths Textbook Solution.

Answers (1)

Answer: \lambda =2

Hint: You must know the rules of vector functions

Given: If D is the mid-point of sides BC of a triangle ABC such \vec{AB}+\vec{AC}=\lambda \vec{AD} find \lambda

Solution: D is mid-point of side BC of a ABC, \vec{AB}+\vec{AC}=\lambda \vec{AD}

Let \vec{a},\vec{b},\vec{c}is a position vectors of AB, BC, CA

            Now, the position vector of D is \frac{\vec{b}+\vec{c}}{2}

            Then,

                        \vec{AB}=\vec{b}-\vec{a}

                        \vec{AC}=\vec{c}-\vec{a}

\begin{gathered} \overrightarrow{A D}=\frac{\vec{b}+\vec{c}}{2}-\vec{a} \\ \therefore \overrightarrow{A B}+\overline{A C}=\lambda \overrightarrow{A D} \\ (\vec{b}-\vec{a})+(\vec{c}-\vec{a})=\lambda\left(\frac{\vec{b}+\vec{c}-2 \vec{a}}{2}\right) \\ \vec{b}-\vec{a}+\vec{c}-\vec{a}=\lambda\left(\frac{\vec{b}+\vec{c}-2 \vec{a}}{2}\right) \\ (\vec{b}+\vec{c}-2 \vec{a})\left(\frac{2}{\vec{b}+\vec{c}-2 \vec{a}}\right)=\lambda \\ \therefore \lambda=2 \end{gathered}

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