The goal of this assignment is to calculate the cross product of the two above vectors.
Click on the correct value that belongs in the empty indicated spot.

The cross product of two vectors results in a vector that is perpendicular to both.
The formula to calculate the cross product a x b, where a and b are both vectors is defined as follows:

a x b = ab sinθn

Where:
- a is the length of vector a, and b is the length of vector b
- θ is the angle between these two vectors
- n is the unit vector that is perpendicular to both a and b. A unit vector means that its length is 1.

Since these values are rather difficult to calculate in most cases, an alternative method exists.
For this, we need the following unit vectors:
i = [1,0,0]
j = [0,1,0]
k = [0,0,1]

The nice thing of these vectors is that with simple scalars x, y and z, you can represent any vector in the following way:
xi + yj + zk = [x, y, z]

The way that is used to calculate a cross product between the vectors [a1, a2, a3] and [b1, b2, b3]
utilizes the following matrix, of which the determinant needs to be calculated:


This leads us to the following determinant:
(a2 * b3 - a3 * b2)i - (a1 * b3 - a3 * b1)j + (a1 * b2 - a2 * b1)k
or:
(a2 * b3 - a3 * b2)i + (a3 * b1 - a1 * b3)j + (a1 * b2 - a2 * b1)k

The goal of this exercise is help you through this process by first filling in this equation, after which calculating the cross product.
The 3D model above is meant to illustrate the concept: the red vector is the first vector,
the blue one the second, and the yellow vector is their cross product.


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