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  • Please Solve R.D.Sharma class 12 Chapter 22 Algbra of Vectors Exercise Very Short Answer Question 9 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 22 Algbra of Vectors  Exercise Very Short Answer Question 9 Maths textbook Solution.

Answers (1)

Answer: 2\left ( \vec{c}-\vec{a} \right )

Hint: You must know the rules of vector functions.

Given: If  \vec{a},\vec{b},\vec{c} are position vectors of points A, B and C respectively, write the value of \vec{AB},\vec{BC},\vec{AC}

Solution: \vec{a},\vec{b},\vec{c}are position vectors of points A, B and C respectively.

            Then,

                    \begin{aligned} &\overrightarrow{A B}=\vec{b}-\vec{a} \\ &\overrightarrow{B C}=\vec{c}-\vec{b} \quad \text { because }[\overline{C A}=\vec{a}-\vec{c}=-\overrightarrow{A C}=\vec{c}-\vec{a}] \text { Opposite direction } \\ &\overline{C A}=\vec{c}-\vec{a} \end{aligned}

Therefore,

\begin{aligned} \overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{A C} &=\vec{b}-\vec{a}+\vec{c}-\vec{b}+\vec{c}-\vec{a} \\ &=2 \vec{c}-2 \vec{a} \\ & \Rightarrow 2(\vec{c}-\vec{a}) \end{aligned}

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