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  • Fill in the blanks The values of k for which ka < a and ka + 1/2a is parallel to a holds true are _______.

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The values 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 _______.

 

Answers (1)

Given that,  |k \vec{a}|<|\vec{a}|

\\ \begin{aligned} &\Rightarrow|k||\vec{a}|<|\vec{a}|\\ &\Rightarrow|k|<1\\ &\Rightarrow-1<k<1\\ &\text { Also, }\\ &k \vec{a}+\frac{1}{2} \vec{a} \text { is parallel to } \vec{a} \end{aligned}

⇒ k cannot be equal to -\frac{1}{2} , otherwise it will become null vector and then it will not be parallel to \vec{a} .

Since, k is along the direction of \vec{a}  and not in its opposite direction.

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

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