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  • Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 21 maths textbook solution

Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 21 maths textbook solution

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Answer:- k \in\left(-1, \frac{1}{2}\right) \cup\left(-\frac{1}{2}, 1\right)  

Hint:-To solve this question, we use magnitude formula.

Given:-The value of k for which |k \vec{a}|<|\vec{a}| \text { and } k \vec{a}+\frac{1}{2} \vec{a}is parallel to \vec{a} holds true are ---

Solution:- |k \vec{a}|<|\vec{a}|

\begin{aligned} &\Rightarrow k|\vec{a}|<|\vec{a}| \\\\ &\Rightarrow k<1 \\ \\&\Rightarrow-1<k<1 k \in(-1,1) \end{aligned}\begin{aligned} &\Rightarrow k|\vec{a}|<|\vec{a}| \\\\ &\Rightarrow k<1 \\ \\&\Rightarrow-1<k<1 k \in(-1,1) \end{aligned}

\begin{aligned} &k \vec{a}+\frac{1}{2} \vec{a} \text { is parallel to } a\\\\ &\text { If we put } k=\frac{-1}{2} \text { then } k \vec{a}+\frac{1}{2} \vec{a} \end{aligned}

\begin{aligned} &=-\frac{1}{2} \vec{a}+\frac{1}{2} \vec{a}=0 \\\\ &k \neq \frac{-1}{2} \end{aligned}

k \in\left(-1, \frac{1}{2}\right) \cup\left(-\frac{1}{2}, 1\right)

 

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