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  • Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 11

Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 11

Answers (1)

Answer:- \vec{c}=3 \vec{b}-2 \vec{a}

Hint:-To solve this equation, we use magnitude length.

Given:- If \vec{a} and \vec{b} are the position vector of A and B respectively, then the position vector of a point Cand AB produced such that \overrightarrow{A C}=3 \overrightarrow{A B}

Solution:-here

\begin{aligned} &\overrightarrow{A B}=\vec{B}-\vec{A}=\vec{b}-\vec{a} \\\\ &\overrightarrow{A C}=\vec{C}-\vec{A}=\vec{c}-\vec{a} \end{aligned}

We have \overrightarrow{A C}=3 \overrightarrow{A B}

        |\overrightarrow{A B}|=x

Then \overrightarrow{A C}=3 x

\frac{A C}{B C}=\frac{m}{n} \rightarrow \bar{c}=\frac{m \vec{b}-n \vec{a}}{m-n}

External dimension

\bar{c}=\frac{3 \vec{b}-2 \vec{a}}{3-2}=\frac{3 \vec{b}-2 \vec{a}}{1}=3 \vec{b}-2 \vec{a}

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