Physics Lesson 2.5.2 - How to calculate the cross product of two vectors?

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Welcome to our Physics lesson on How to calculate the cross product of two vectors?, this is the second lesson of our suite of physics lessons covering the topic of Vector Product of Two Vectors, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

How to calculate the cross product of two vectors?

From geometry, it is known that the area of a parallelogram is calculated by the formula

Area = Base × Height

Look at the figure below:

Physics Tutorials: This image shows the area of a parallelogram

From Trigonometry, it is known that

Opposite side of triangle = Hypotenuse × sin θ

Here, Opposite side of triangle = Height of parallelogram and Hypotenuse = Lateral side of parallelogram. Therefore, we obtain

Area of parallellogram = Base × Lateral side × sin θ

Substituting the Base and Lateral side with the lengths of vectors a⃗ and b⃗ respectively as shown in the figure below,

Physics Tutorials: This image shows a parrelelogram to help explain vector calculations using trogonometry

we obtain:

|c⃗| = |a⃗| × |b⃗| × sin θ

But we stated before that

c⃗ = a⃗ × b⃗

and since it is obvious that the above equation is true for magnitudes as well, i.e.

|c⃗| = |a⃗×b⃗|

we obtain

|c⃗| = |a⃗×b⃗| = |a⃗| × |b⃗| × sin θ

You have reach the end of Physics lesson 2.5.2 How to calculate the cross product of two vectors?. There are 6 lessons in this physics tutorial covering Vector Product of Two Vectors, you can access all the lessons from this tutorial below.

More Vector Product of Two Vectors Lessons and Learning Resources

Vectors and Scalars Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
2.5	Vector Product of Two Vectors
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
2.5.1	The meaning of cross product of vectors multiplication
2.5.2	How to calculate the cross product of two vectors?
2.5.3	What is the direction of the vector product obtained by the cross product of two vectors?
2.5.4	Cross product of vectors in coordinates
2.5.5	Applications of cross product in Physics
2.5.6	Mixed product of vectors

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