Multiplying a vector by a scalar results in:

a) a scalar
b) a perpendicular vector
c) a collinear vector
c) a parallel scalar

a

Multiplying a vector by a scalar results in a collinear vector.

To understand why, let's start with the definitions. A scalar is a single value that has only magnitude, such as a number. A vector, on the other hand, has both magnitude and direction, and it is represented by an arrow.

When we multiply a vector by a scalar, we are essentially scaling the vector by that value. This means that every component of the vector is multiplied by the scalar.

For example, let's say we have a vector v with components (x, y, z), and we multiply it by a scalar k. The resulting vector v' would be (k * x, k * y, k * z).

Now, let's consider what happens to the direction of the vector. Since we multiply each component of the vector by the scalar, the ratios between the components remain the same. This means that the direction of the vector does not change; it remains parallel to the original vector.

However, the magnitude of the resulting vector changes. It becomes equal to the magnitude of the original vector multiplied by the scalar. In other words, if the original vector had a length of "L," the resulting vector has a length of "k * L."

Therefore, we can conclude that multiplying a vector by a scalar results in a collinear vector - a vector that has the same direction but a different magnitude.