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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise 22.3 Question 4 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise 22.3 Question 4 Maths Textbook Solution.

Answers (1)

Answer: 3\vec{b}-2\vec{a},2\vec{a}-\vec{b}

Hint: Vector law of addition,  (two vectors one represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector.)

Given: \vec{AC}=3\vec{AB}

Solution:

    

In \triangle \mathrm{OAB},

=\overrightarrow{O A}+\overrightarrow{A B}=\overrightarrow{O B}\: (By \: triangle\: law \: of \: vector \: addition)

\mathrm{AB}=\vec{b}-\vec{a}

In \triangle \mathrm{OAC}

=\overrightarrow{O C}=\overrightarrow{O A}+\overrightarrow{A C}     (By\: triangle \: law \: of\: vector \: addition)

 

=\overrightarrow{O A}+3 \overrightarrow{A B} \      [ given \overrightarrow{A C}=3 \overrightarrow{A B}]

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

=3 \vec{b}-2 \vec{a}

\text{Again in }\triangle O A D

\overrightarrow{O D}=\overrightarrow{O A}+\overrightarrow{A D} \ \ \ (\text{ By triangle law of vector addition})

=\vec{a}+\vec{a}-\vec{b} \quad[\because \overrightarrow{A D}=-\overrightarrow{A B}]

=2 \vec{a}-\vec{b}

 

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