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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 25 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 25 Maths Textbook Solution.

Answers (1)

Answer: -\hat{i}+5\hat{j}-12\hat{k}

Hint: You must know the rules of vector functions

Given: Find position vector of point dividing line segment

\hat{i}+\hat{j}-2\hat{k},2\hat{i}-\hat{j}+3\hat{k} Externally in 2:3

Solution: Let A and B be the points with vectors

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

Let C divide AB externally with ratio 2:3 such AC: CB=2:3

Position vector of C=

                             \begin{aligned} &=\frac{2(2 \hat{i}-\hat{j}+3 \hat{k})-3(\hat{i}+\hat{j}-2 \hat{k})}{2-3} \\ &=\frac{(4 \hat{i}-2 \hat{j}+6 \hat{k})-3 \hat{i}-3 \hat{j}+6 \hat{k}}{-1} \\ &=\frac{1}{-1}(\hat{i}-5 \hat{j}+12 \hat{k}) \\ &=-\hat{i}+5 \hat{j}-12 \hat{k} \end{aligned}

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