Problem 68 - Algebra and Trigonometry

Question

What are parallel vectors?

Step-by-Step Solution

Answer

Parallel vectors are vectors that share the same direction or are oppositely directed. They are actually scalar multiples of each other.

Step 1: Definition

Parallel vectors are vectors that share the same or opposite direction. They have the property that one vector is a scalar multiple of the other. If \( \vec{a} \) and \( \vec{b} \) are parallel vectors, we can write this as \( \vec{a} = k\vec{b} \), where k is a scalar.

Step 2: Direction

Parallel vectors maintain the same angle at any point in space. That is to say, the angle between parallel vectors is always 0 degrees or 180 degrees (if they are in opposite directions)

Step 3: Applications

This concept of parallel vectors is widely used in physics and engineering, for instance, in determining force vectors, and in the study of electric field intensity and magnetic fields, among others.