How do I find the vector/cross product of two three-dimensional vectors?
Finding the cross product of two 3D vectors uses a very similar method to that of finding the determinant of a 3x3 matrix.
So, to find the cross product, just follow these simple steps:
- To begin, create a 3x3 matrix with the unit vectors i, j and k filling the top row.
- Take the first vector and put the x component under the i, the y component under the j and the z component under the k. Repeat this for the second vector by putting the x, y and z components in their correct columns in the bottom row of the matrix.
- Next, cover the first row and the first column (the row and column containing the i unit vector). This leaves a 2x2 matrix still showing. You should find the determinant of this matrix (remember from FP1: determinant = ad-bc). This determinant then becomes the x component of the final vector we are trying to find.
- Now uncover the first row and column and cover the row and column containing the j unit vector. Find the determinant of the resulting 2x2 matrix and then multiply the determinant by -1. This becomes the y component of the final vector.
- Repeat this for the k unit vector, but without multiplying by -1, to find the z component of the final vector.
- You now have the final vector - this is the vector product of your original vectors!
Remember: You only have to multiply the y component (when you cover the j) by -1!
LM
Answered by Luke M. • Further Mathematics tutor
7507 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Given that y = cosh^-1 (x) , Show that y = ln(x+ sqrt(x^2-1))
Solve (z-i)+(z+i)+(z-1)+(z-1)
It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.
The plane Π contains the points (1, 2, 3), (0, 1, 2) and (2, 3, 0). What is the vector equation of the plane? and what is the cartesian equation of the plane?