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

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

Answers (1)

Answer: \frac{1}{3}\left ( 2\vec{b}+\vec{a} \right )

Hint: You must know the rules of vector functions

Given: If \vec{a} & \vec{b}denote the position vectors of points A and B respectively and C is appoint on AB, such that 3AC = 2AB, then write the position vector of C

Solution: Let \vec{c}is the position vector of c

Now,

        \vec{AB}=\vec{b}-\vec{a}

        \vec{AC}=\vec{c}-\vec{a}

Consider,

                \begin{aligned} &3 \overrightarrow{A C}=2 \overrightarrow{A B} \\ &3(\vec{c}-\vec{a})=2(\vec{b}-\vec{a}) \\ &3 \vec{c}-3 \vec{a}=2 \vec{b}-2 \vec{a} \\ &3 \vec{c}=2 \vec{b}-2 \vec{a}+3 \vec{a} \\ &3 \vec{c}=2 \vec{b}+\vec{a} \\ &\vec{c}=\frac{1}{3}(2 \vec{b}+\vec{a}) \end{aligned}

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