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  • Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 15

Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 15

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Answer:-  \frac{1}{3}

Hint:-To solve this we know that two lines are collinear

Given:-The vector \vec{a} and \vec{b} are non collinear if (x-2) \vec{a}+\vec{b} \text { and }(2 x+1) \vec{a}-\vec{b} are collinear then x……

Solution:- Let a_{1} x+b_{1} y+c_{1}=0, a_{2} x+b_{2} y+c_{2}=0

For collinear

\begin{aligned} &\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} \\\\ &\vec{c}=(x-2) \vec{a}+\vec{b} \\\\ &\vec{b}=(2 x+1) \vec{a}-\vec{b} \end{aligned}

Hence

\begin{aligned} \\ &\frac{x-2}{2 x+1}=\frac{1}{-1}\\\\ &-x+2=2 x+1\\\\ &2-1=2 x+x \end{aligned}

\begin{aligned} &1=3 x \\\\ &x=\frac{1}{3} \end{aligned}

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