To find the cross product of two vectors, enter the coordinates or points of both vectors in the cross product calculator.
This vector multiplication calculator aka cross multiply calculator helps to find the resultant vector of two given vectors. You can click on the “show more” option to see the step-by-step solution.
This vector calculator allows you to input information in the form of coordinates as well as points of the vector.
Vectors can be multiplied to find the resultant vector. There are two ways to multiply a pair of vectors.
Cross product is defined as:
“Cross products only work in 3D. It measures how much two vectors point in different directions.”
It is represented by A x B (read as A cross B).
A x B = A*B sin
The formula used for vector cross product is a little complex. Firstly, the vectors are written in the form of a matrix. The first row of the matrix is of unit vectors.
i j k
ax ay az
bx by bz
After this step, this matrix is expanded.
There are certain properties of cross-product which differ it from the dot product.
The process of vector multiplication can be more easily understood through an example.
Find the cross product of the following vectors.
A = 3i + 2j + 1k
B = 1i + 2j + 3k
Step 1: Write vectors in the form of coordinates.
A = (3,2,1)
B = (1,2,3)
Step 2: Form the matrix.
i j k
3 2 1
1 2 3
Step 3: Expand the matrix.
= i[(2).(3) - (1).(2)] - j[(3).(3) - (1).(1)] + k[(3).(2) - (2).(1)]
= i[(6) - (2)] - j[(9) - (1)] + k[(6) - (2)]
= 4i - 8j + 4k