The magnitude of the resultant of two vectors lies between the range of their sum and the difference. For vectors of magnitudes 4 units and 8 units, the possible resultant must be between:
\(\ \ |8 - 4| = 4 \text{units} \quad \text{and} \quad 8 + 4 = 12 \text{units}.\)
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 
Choose the correct answer from the options given below:
For x < 0:
f(x) = ex + ax
For x ≥ 0:
f(x) = b(x - 1)2