If the angle between the vectors `vec(a)` and `vec(b)` is an acute angle, then the diffrence `vec(a)-vec(b)` is

Options

A. The major diagonal of the parallelogram
B. The minor diagnol of the parallelogram
C. Any of the above
D. None of the above

Explanation

To solve the problem, we need to analyze the vectors \(\vec{a}\) and \(\vec{b}\) and their relationship when the angle between them is acute. Here’s a step-by-step solution:

### Step 1: Understand the Vectors
We have two vectors, \(\vec{a}\) and \(\vec{b}\), with an acute angle \(\theta\) between them. An acute angle means \(0 < \theta < 90^\circ\).

**Hint:** Remember that an acute angle is less than 90 degrees.

### Step 2: Visualize the Vectors
Draw the vectors \(\vec{a}\) and \(\vec{b}\) originating from the same point. Since the angle is acute, \(\vec{b}\) will be positioned such that it is within the first quadrant relative to \(\vec{a}\).

**Hint:** Sketch the vectors on a coordinate plane to visualize their positions.

### Step 3: Construct the Parallelogram
To find \(\vec{a} - \vec{b}\), we can use the parallelogram law. Draw \(\vec{b}\) in the opposite direction to get \(-\vec{b}\). Now, you can form a parallelogram with \(\vec{a}\) and \(-\vec{b}\).

**Hint:** The diagonal of the parallelogram formed by \(\vec{a}\) and \(-\vec{b}\) represents the vector \(\vec{a} - \vec{b}\).

### Step 4: Analyze the Resulting Vector
The diagonal that represents \(\vec{a} - \vec{b}\) will be the minor diagonal of the parallelogram. Since \(\vec{a}\) is longer than \(\vec{b}\) (as the angle is acute), \(\vec{a} - \vec{b}\) will also point in the same general direction as \(\vec{a}\).

**Hint:** The direction of \(\vec{a} - \vec{b}\) will be similar to that of \(\vec{a}\) because \(\vec{a}\) is greater than \(\vec{b}\).

### Step 5: Conclusion
Since \(\vec{a}\) is greater than \(\vec{b}\) and the angle between them is acute, the resultant vector \(\vec{a} - \vec{b}\) will also be a vector pointing in the same direction as \(\vec{a}\) but with a smaller magnitude than \(\vec{a}\).

**Final Answer:** The difference \(\vec{a} - \vec{b}\) is a vector that points in the same direction as \(\vec{a}\) and has a magnitude less than that of \(\vec{a}\).