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  • Need solution for RD Sharma Maths Class 12 Chapter 22 Algera of Vectors Excercise 22.7 Question 3

Need solution for RD Sharma Maths Class 12 Chapter 22 Algera of Vectors Excercise 22.7 Question 3

Answers (1)

Answer:

Point A, B and C are collinear

Hint:

Obtain the parallel vectors and if any common points is there they are parallel to each other

Given:

Three vectors are given.        

Solution:

Let,

\begin{aligned} &A=\hat{i}+2 \hat{j}+3 \hat{k}\\ & \end{aligned}

B=3 \hat{i}+4 \hat{j}+7 \hat{k}\\

C=-3 \hat{i}-2 \hat{j}-5 \hat{k}\\

\therefore \overrightarrow{A B}=(3 \hat{i}+4 \hat{j}+7 \hat{k})-(\hat{i}+2 \hat{j}+3 \hat{k})\\

=(3-1) \hat{i}+(4-2) \hat{j}+(7-3) \hat{k}\\

=2 \hat{i}+2 \hat{j}+4 \hat{k}                                         … (i)

Similarly

\begin{aligned} &\overrightarrow{B C}=(-3 \hat{i}-2 \hat{j}-5 \hat{k})-(3 \hat{i}+4 \hat{j}+7 \hat{k})\\ & \end{aligned}

=(-3-3) \hat{i}+(-2-4) \hat{j}+(-5-7) \hat{k}\\

=-6 \hat{i}-6 \hat{j}-12 \hat{k}\\

=-6(\hat{i}+\hat{j}+2 \hat{k})\\

\begin{aligned} &\overrightarrow{B C}=-3(2 \hat{i}+2 \hat{j}+4 \hat{k}) \end{aligned}              … (ii)

Put (i) in (ii)

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

From above result, B is the common point in  \overline{A B} \& \overline{B C}

A, B and C points are collinear.

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