The vectors `veca and vecb ` are non collinear. Find for what value of x the vectors `vecc=(x-2)veca+vecb and vecd=(2x+1) veca-vecb` are collinear.?

Explanation

To determine the value of \( x \) for which the vectors \( \vec{c} = (x-2)\vec{a} + \vec{b} \) and \( \vec{d} = (2x+1)\vec{a} - \vec{b} \) are collinear, we can use the property that two vectors are collinear if the ratios of their corresponding components are equal.

### Step-by-Step Solution:

1. **Set Up the Ratios**: For the vectors \( \vec{c} \) and \( \vec{d} \) to be collinear, we can express this condition as:
\[ \frac{x-2}{2x+1} = \frac{1}{-1} \]
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