Answer is infinite.
Yes! There are infinite vectors perpendicular to a single vector in 3D space.
To visualise it just hold a pencil in your hand such that it's tip acts as the head of the vector.Now use your finger to make a perpendicular vector to the pencil.
You will find you can rotate ur finger around the penciland thus you will get infinite vectors perpendicular to the pencil.

Perpendicular Vector to 4i-3j
The vector 4i-3j lies in the xy-plane, with components along the x and y axes. To find a vector perpendicular to 4i-3j, we can use the properties of dot product and cross product.

Using Dot Product:
- Let the perpendicular vector be a(xi + yj).
- To find the perpendicular vector, we need to ensure that the dot product of 4i-3j and a(xi + yj) is zero.
- The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them.
- Setting up the dot product equation: 4a - 3b = 0, where a and b are the components of the perpendicular vector.
- Solving this equation gives us the perpendicular vector.

Using Cross Product:
- Another method to find a perpendicular vector is by taking the cross product of 4i-3j with a vector in the z-direction.
- The cross product of two vectors gives a vector that is perpendicular to both input vectors.
- Taking the cross product of 4i-3j and k (unit vector in the z-direction) gives us the perpendicular vector.
By using either of these methods, we can determine a vector that is perpendicular to 4i-3j.