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 ______.

Answer 1

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`.