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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 20 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 20 Maths Textbook Solution.

Answers (1)

Answer: 3 \hat{i}+\frac{11}{3} \hat{j}+5 \hat{k}

Hint: You must know the rules of vector functions

Given: Write the position vector of a point dividing the line segment joining points A and B with position vectors \vec{a} &\vec{b} externally in the ratio 1:4 , where,

\begin{aligned} &\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k} \\ &b=-\hat{i}+\hat{j}+\hat{k} \end{aligned}

Solution: The position vectors of A and B are

\begin{aligned} &\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k} \\ &b=-\hat{i}+\hat{j}+\hat{k} \end{aligned}

Let C divides AB in the ratio such that AB:CB=1:4

   Position vector of C=

\begin{aligned} &\frac{1(-\hat{i}+\hat{j}+\hat{k})-4(2 \hat{i}+3 \hat{j}+4 \hat{k})}{1-4} \\ &\Rightarrow \frac{-\hat{i}+\hat{j}+\hat{k}-8 \hat{i}-12 \hat{j}-16 \hat{k}}{-3} \\ &\Rightarrow \frac{-9 \hat{i}-11 \hat{j}-15 \hat{k}}{-3} \Rightarrow 3 \hat{i}+\frac{11 \hat{j}}{3}+5 \hat{k} \end{aligned}

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