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  • Please Solve R.D.Sharma class 12 Chapter 22 Algbra of Vectors Exercise 22.3 Question 1 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 22 Algbra of Vectors  Exercise 22.3 Question 1 Maths textbook Solution.

Answers (1)

Answer:

\frac{5}{3}\vec{a},3\vec{a}+4\vec{b}

Hint: if a point R divides a line PQ into m:n internally then point P=\frac{m\vec{OR+n\vec{OP}}}{m-n}and externally then point R=\frac{m\vec{OQ+n\vec{OP}}}{m-n}

Given:

\vec{OP}=2\vec{a}+\vec{b}

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

Solution:

(i) \overrightarrow{O R}( internally )

=\frac{1(\vec{a}-2 \vec{b})+2(2 \vec{a}+\vec{b})}{1+2}

=\frac{\vec{a}-2 \vec{b}+4 \vec{a}+2 \vec{b}}{3}

=\frac{5 \vec{a}}{3}

(ii) \overrightarrow{O R}( Externally )

=\frac{1(\vec{a}-2 \vec{b})-2(2 \vec{a}+\vec{b})}{1-2}

=\frac{\vec{a}-2 \vec{b}-4 \vec{b}-2 \vec{b}}{-1}

=\frac{-3 \vec{a}-4 \vec{b}}{-1}

=3 \vec{a}+4 \vec{b}

 

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