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Question
The values of k for which `|"k"vec"a"| < |vec"a"|` and `"k"vec"a" + 1/2 vec"a"` is parallel to `vec"a"` holds true are ______.
Solution
The values of k for which `|"k"vec"a"| < |vec"a"|` and `"k"vec"a" + 1/2 vec"a"` is parallel to `vec"a"` holds true are `"k" ∈(-1, 1) and "k" ≠ 1/2`.
Explanation:
Given that `|"k"vec"a"| < |vec"a"|` and `"k"vec"a" + 1/2 vec"a"` is parallel to `vec"a"`
∴ `|"k"vec"a" + 1/2 vec"a"` is parallel to when `"k" ∈(-1, 1) and "k" ≠ 1/2`.
Hence, the required value of `"k" ∈(-1, 1) and "k" ≠ 1/2`.
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