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  • Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.7 Question 9 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.7 Question 9 Maths Textbook Solution.

Answers (1)

Answer:

Given points are collinear

Hint:

If the points are collinear then they are parallel.

Given:

(3,4),(-5,16) \&(5,1)  Are collinear

Solution:

Let,

\begin{aligned} &A=3 \hat{i}+4 \hat{j} \\ &B=-5 \hat{i}+16 \hat{j} \\ &C=5 \hat{i}+\hat{j} \end{aligned}

\therefore \overrightarrow{A{B}}=  Position of B – Position of A

=(-5 \hat{i}+16 \hat{j})-(3 \hat{i}+4 \hat{j}) \\

=(-5-3) \hat{i}+(16-4) \hat{j} \\

=-8 \hat{i}+12 \hat{j} \\

\begin{aligned} & &=-4(2 \hat{i}-3 \hat{j}) \end{aligned}                         … (i)

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

=(\hat{5} \hat{i}+\hat{j})-(-5 \hat{i}+16 \hat{j}) \\

=(5+5) \hat{i}+(1-16) \hat{j} \\

=10 \hat{i}-15 \hat{j} \\

\begin{aligned} & &=5(2 \hat{i}-3 \hat{j}) \end{aligned}                            … (ii)

From (i) and (ii)

\overrightarrow{B C}=\frac{-5}{4} \overrightarrow{A B}

Thus  \overrightarrow{B C} \& \overrightarrow{A B}  are parallel to each and B being the common point

A, B and C are collinear

Thus, (3,4),(-5,16) \&(5,1)  are collinear

 

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