Cross Product of Two Vectors Explained!

TL;DR

Learn how to find the cross product of two vectors and check if the resulting vector is perpendicular to the original vectors.

Transcript

in this video we're going to talk about how to find the cross product of two vectors so let's say if vector a is 3i plus 5j minus 7k and vector b is 2i minus 6j plus 4k so what is the cross product of vectors a and b how can we find the answer what i'd like to do is first put this in the form of a matrix this is i j k which corresponds to the x y a... Read More

Key Insights

• 😵 The cross product of two vectors is found by evaluating the determinant of a 3x3 matrix.
• 🫥 Perpendicular vectors have a dot product of zero.
• 😵 The cross product of two vectors is another vector that is perpendicular to both input vectors.

Questions & Answers

Q: How can we find the cross product of two vectors?

To find the cross product, form a 3x3 matrix with the vectors and evaluate the determinant.

Q: How do we evaluate the determinant of a 2x2 matrix?

Multiply the diagonal elements and subtract the product of the off-diagonal elements.

Q: How can we check if the resulting vector is perpendicular to the original vectors?

Calculate the dot product of each original vector with the resulting vector, which should be zero if they are perpendicular.

Q: What if the dot product of the original vectors and the resulting vector is not zero?

If the dot product is not zero, then the resulting vector is not perpendicular to the original vectors.

Summary & Key Takeaways

• The cross product of two vectors can be found by evaluating the determinant of a 3x3 matrix formed by the two vectors.

• To find the determinant of a 2x2 matrix, multiply the diagonal elements and subtract the product of the off-diagonal elements.

• The dot product of the resulting vector and the original vectors should be zero to confirm that the resulting vector is perpendicular to the original vectors.