This is a "relevant equation" only if you say what v1 and v2 are! In particular are you clear that v1 and v2 are NOT the "two linearly independent vectors" of the question? Call the two vectors u and v. Their sum is u+ v and their difference is u- v. So "their sum is perpendicular to their difference" means (u+ v).(u- v)= 0. What does the fact that they are linearly independent tell you?noahsdev said:Homework Statement
If two linearly independent vectors are of equal magnitude, prove that their sum is perpendicular to their difference.
Homework Equations
v1.v2 = 0
The Attempt at a Solution
This question doesn't seem that hard but it's really confused me.
Help is appreciated, thanks.
A vector is a mathematical quantity that has both magnitude (size/length) and direction. It is commonly represented by an arrow in a coordinate system.
To add two vectors, you must add their components (magnitude and direction) separately. The resulting vector will have a magnitude equal to the sum of the magnitudes of the original vectors, and a direction determined by the angle between the two original vectors.
A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, time, and mass, while examples of vectors include displacement, velocity, and force.
Yes, vectors can have negative components. This indicates that the vector is pointing in the opposite direction of the positive component. For example, a vector with a negative x-component is pointing in the negative x-direction.
Vectors have many practical applications in real life, such as in navigation and mapping, physics and engineering, and computer graphics. They are also used in sports, such as in calculating the trajectory of a baseball or the velocity of a moving object.