Vectors - Determinant Method Cross Product

Description:

Cross Product – Determinant Method

• As a student, you will study about determinants in detail in Mathematics.

• For now, let’s try and understand basic approach of solving a determinant and its usefulness in calculating cross product with speed.

• Determinant method is only applicable when the two vectors are in their resolved form.

• Therefore, let’s say, a→ = (a_x î + a_y ĵ + a_z k̂)

• Also, b→ = (b_x î + b_y ĵ + b_z k̂)

• A determinant should be created in the following way −

This should be solved step by step as shown below −

• First step

This should be expanded as −

î(a_yb_z - a_zb_y)

• Second step

This should be expanded as −

- ĵ(a_xb_z - a_zb_x)

• Third step

k̂(a_xb_y - a_yb_x)

• All the terms should be added. Hence, the cross-product value is −

P→ = (a_yb_z - a_zb_y) î - (a_xb_z - a_zb_x) ĵ + (a_xb_y - a_yb_x) k̂