`veca` and `vecb` are two given vectors. On these vectors as adjacent sides a parallelogram is constructed. The vector which is the altitude of the parallelogam and which is perpendicular to `veca` is not equal to

Options

A. `((veca.vecb))/(|veca|^(2))veca-vecb`
B. `1/|veca|^(2){|veca|^(2)vecb- (veca.vecb)veca}`
C. `(vecaxx(veca xx vecb))/(|veca|^(2))`
D. `(vecaxx(vecb xx veca))/(|vecb|^(2))`

Explanation

To solve the problem, we need to determine which vector is not equal to the altitude of the parallelogram constructed on vectors \(\vec{a}\) and \(\vec{b}\).

### Step-by-Step Solution:

1. **Understanding the Parallelogram**:
We have two vectors \(\vec{a}\) and \(\vec{b}\) that form adjacent sides of a parallelogram. Let's denote the vertices of the parallelogram as \(A\), \(B\), \(C\), and \(D\) where \(AB = \vec{a}\) and \(AD = \vec{b}\).

2. **Identifying the Altitude**:
The altitude of the parallelogram from vertex \(D\) to side \(AB\) is the perpendicular distance from point \(D\) to line \(AB\). Let's denote the foot of the perpendicular from \(D\) to line \(AB\) as point \(M\).

3. **Finding the Projection**:
The vector \(AM\) represents the projection of vector \(\vec{b}\) onto vector \(\vec{a}\). The formula for the projection of \(\vec{b}\) onto \(\vec{a}\) is given by:
\[ \text{proj}_{\vec{a}} \vec{b} = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2} \vec{a} \]
Thus, we have:
\[ \vec{AM} = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2} \vec{a} \]

4. **Finding the Vector \(MD\)**:
The vector \(MD\) can be found using the triangle law of vector addition:
\[ \vec{AD} = \vec{AB} + \vec{AM} \implies \vec{MD} = \vec{AD} - \vec{AM} = \vec{b} - \frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2} \vec{a} \]

5. **Expressing the Altitude Vector**:
The altitude vector \(\vec{DM}\) can be expressed as:
\[ \vec{DM} = -\vec{MD} = -\left(\vec{b} - \frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2} \vec{a}\right) \]
Simplifying gives:
\[ \vec{DM} = -\vec{b} + \frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2} \vec{a} \]

6. **Identifying the Incorrect Option**:
We need to check which of the given options does not match the expression for \(\vec{DM}\). The options provided will typically consist of various combinations of \(\vec{a}\) and \(\vec{b}\).

After checking the options:
- If options 1, 2, and 3 match the derived expression for \(\vec{DM}\), then option 4 is the one that does not represent the altitude.

### Conclusion:
The vector that is not equal to the altitude of the parallelogram constructed on vectors \(\vec{a}\) and \(\vec{b}\) is **option 4**.