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Fill in the blanks:

The values of k for which \(|k \vec a| < | \vec a|\) and \(k \vec a + \frac{1}{2} \vec a\) is parallel to \(\vec a \) holds true are _______.

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⇒ k cannot be equal to -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.

∴ k ∈ (-1,1) – {-1/2}

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