Vector Basics

Magnitude of Vector Sum and Difference

Let the two vectors be and with magnitudes and , respectively. Then, the magnitude of their sum is given by:

(\)

Where is the angle between the vectors.

The magnitude of their difference is given by:

(\)

Now, according to the question, we are given that:

From this, we have:

Simplifying the above equation:

This gives us:

Thus, the angle between the two vectors is:

Conclusion:

The angle between the vectors and is , meaning the vectors are perpendicular to each other.