If vectors a and b are given as a = (2, -4, 4) and b = (4, 0, 3), what is the magnitude of the resultant vector c after performing the cross product?

To find the magnitude of the resultant vector (c) after performing the cross product of vectors (a) and (b), you can use the formula for the magnitude of the cross product, which is given by:

[

|c| = |a \times b| = |a| \cdot |b| \cdot \sin(\theta)

]

where (\theta) is the angle between the vectors (a) and (b). However, it is often easier to directly compute the cross product using the determinant of a matrix formed by the vectors.

For (a = (2, -4, 4)) and (b = (4, 0, 3)), we can find the cross product (c = a \times b) using the following determinant:

[

c = \begin{vmatrix}

\hat{i} & \hat{j} & \hat{k} \

2 & -4 & 4 \

4 & 0 & 3

\end{vmatrix}

]

Calculating this determinant will yield:

[

c = \hat{i}((-4)(3) - (4)(0)) - \