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  • Please Solve R.D. Sharma class 12 Chapter 22 Algbra of Vectors Exercise 22.2 Question 3 Maths textbook Solution.

Please Solve R.D. Sharma class 12 Chapter 22 Algbra of Vectors  Exercise 22.2 Question 3 Maths textbook Solution.

Answers (1)

Answer:

\vec{a}+\vec{b} and \vec{d}-\vec{b} are the diagonals of parallelogram. whose adjacent sides are \vec{a} and \vec{b}

Hint:

Use triangle law of vector.

Given :

\vec{a},\vec{b},\vec{c}are three sides of triangle

Solution:

\vec{a} and \vec{b} are two collinear vectors having the same initial point.                                   

Let AB= \vec{a} and AD= \vec{b}

let us draw a parallelogram with AB and AD as any of two sides of the parallelogram.

We know in parallelogram opposite sides are equal hence,

DC= \vec{a} and BC= \vec{b}

Now consider \Delta ABC , applying

Triangle law of vector we got,        

\begin{aligned} &\overrightarrow{A B}+\overrightarrow{B C}=\overrightarrow{A C}\\ &\vec{a}+\vec{b}=\overrightarrow{A C}\\ \end{aligned}

Similarly in \Delta ABD

\begin{aligned} &\overrightarrow{A D}+\overrightarrow{D B}=\overrightarrow{A B}\\ &\vec{b}+D B=\vec{a}\\ &\therefore \vec{a}-\vec{b}=\overrightarrow{D B} \end{aligned}

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