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  • Provide Solution for RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.7 Question 6

Provide Solution for RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.7 Question 6

Answers (1)

Answer:

A, B and C are collinear points

Hint:

From the origin, point O towards a point ‘A’.  \overrightarrow{O A}=-\overrightarrow{A O}

 

Given:

A, B and C are collinear

Solution:

As per shown figure above

\begin{aligned} \overrightarrow{O A} &=-\overrightarrow{A O} \\ \overrightarrow{O B} &=-\overrightarrow{B O} \\ \overrightarrow{O C} &=-\overrightarrow{C O} \end{aligned}

Where O must be the origin

We have,

\begin{aligned} &\overrightarrow{A O}+\overrightarrow{O B}=\overrightarrow{B O}+\overrightarrow{O C} \\ &\overrightarrow{A O}-\overrightarrow{B O}=\overrightarrow{O C}-\overrightarrow{O B} \\ &(-\overrightarrow{O A})-(-\overrightarrow{O B})=\overrightarrow{O C}-\overrightarrow{O B} \\ &\overrightarrow{O B}-\overrightarrow{O A}=\overrightarrow{O C}-\overrightarrow{O B} \end{aligned}

From above figure we can say

\overrightarrow{A B}=\overrightarrow{B C}

 

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