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

Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.7 Question 2 Subquestion (ii) 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:

\vec{a}, \vec{b} \& \vec{c}  Are non-coplanar vectors    

Solution:

Let, points A, B and C be the position vectors for  \vec{a}+\vec{b}+\vec{c}, 4 \vec{a}+3 \vec{b}, 10 \vec{a}+7 \vec{b}-2 \vec{c}  respectively

\overrightarrow{A B}  Position vector B – Position vector A

=(4 \vec{a}+3 \vec{b})-(\vec{a}+\vec{b}+\vec{c}) \\

=3 \vec{a}+2 \vec{b}+(-\vec{c}) \\

\begin{aligned} & &\overrightarrow{A B}=3 \vec{a}+2 \vec{b}-\vec{c} \end{aligned}                           …(i)

Similarly,

\begin{aligned} &\overrightarrow{B C}=(10 \vec{a}+7 \vec{b}-2 \vec{c})-(4 \vec{a}+3 \vec{b})\\ & \end{aligned}

=6 \vec{a}+4 \vec{b}-2 \vec{c}\\

=2(3 \vec{a}+2 \vec{b}-\vec{c})                           …(ii)

Substitute (i) in (ii)

\therefore \overline{B C}=2 \overrightarrow{A B}

Hence, \overrightarrow{A B} \& \overline{B C}  are parallel vectors.

As B point is common in both vectors

Thus, A, B and C are collinear points.

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