**Given Information:**
We are given two vectors with magnitudes 3 units and 5 units. The resultant vector is perpendicular to a vector with a magnitude of 3 units.

**To Find:**
We need to find the angle between the two vectors.

**Solution:**
Let's assume the two vectors as vector A and vector B.

1. Let's first find the resultant vector R by adding vector A and vector B.
- R = A + B

2. Since the resultant vector R is perpendicular to a vector with magnitude 3 units, we can use the concept of dot product to find the angle between R and a vector with magnitude 3 units.
- The dot product of two vectors A and B is given by: A · B = |A| |B| cosθ
- Here, |A| represents the magnitude of vector A, |B| represents the magnitude of vector B, and θ represents the angle between the two vectors.

3. We know that the magnitude of vector A is 3 units. So, |A| = 3.
- |B| is given as 5 units.

4. By substituting the known values, we have: 3 · 5 · cosθ = 3 · 3 · cosθ

5. Now, let's solve for cosθ:
- 15 · cosθ = 9 · cosθ
- Subtracting 9 · cosθ from both sides, we get: 15 · cosθ - 9 · cosθ = 0
- Simplifying, we have: 6 · cosθ = 0

6. To find the value of cosθ, we set the equation equal to zero:
- cosθ = 0

7. The value of cosθ is equal to zero when θ is equal to 90 degrees. Therefore, the angle between the two vectors is 90 degrees.

**Answer:**
The angle between the two vectors is 90 degrees.

(a) 127 degree