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  • Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.7 Question 2 Subquestion (i) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.7 Question 2 Subquestion (i) Maths Textbook Solution.

Answers (1)

Answer:

Point A, B and C are collinear

Hint:

Prove, that the position vectors are parallel to each other.

Given:

Point A, B and C with position vectors \vec{a}, \vec{b} \text { and } 3 \vec{a}-2 \vec{b}  respectively            

Solution:

So, \overrightarrow{A B}=  Position of B vector – Position of A vector

\overrightarrow{A B}=\vec{b}-\vec{a}                                    …(i)

Similarly find \overrightarrow{B C}

\overrightarrow{B C}=  Position of C vector – Position of B vector

\begin{aligned} &=(3 \vec{a}-2 \vec{b})-(\vec{b}) \\ & \end{aligned}

=3 \vec{a}-2 \vec{b}-\vec{b}

=3 \vec{a}-3 \vec{b}

\begin{aligned} &=3(\vec{a}-\vec{b}) \\ \end{aligned}

=-3(\vec{b}-\vec{a})                                     …(ii)

Substituting (i) in (ii)

Thus, \overrightarrow{B C}=-3 \overrightarrow{A B}

So we say that \overrightarrow{B C}\; \text{and}\; \overrightarrow{A B}  parallel to each other.

Here B is a common point in both vector

Thus, point A, B and C are collinear

 

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