Sec1Sess7

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dot product of A and B creates matrix with first row as vector with variables <math>\hat{i}, \hat{j}, and\ \hat{k}</math>

<math>\hat{i}, \hat{j}, and\ \hat{k}</math> are used to denote the first column values that are created from the determinants of the values not in the same
row or col as the <math> \langle \widehat{variable} \rangle </math> i.e. <math>\hat{i}</math> .

length: distance in space of vector A and vector B with euclidean distance formula?

Cross product, A x B, is a vector perpendicular to the plane of A and B
example of way to calculate it:
For A = <a1, a2, a3> and B = <b1, b2, b3>:
A x B = (a2*b3 − a3*b2)*i - (a3*b1 − a1*b3)*j + (a1*b2 − a2*b1)*k
+ and - between determinants in crossproduct follow checkerboard pattern
direction: dir(A*B): dir() is cross product formula described earlier that creates a vector perpendicular to vectors A and B
IMPORTANT NOTE: Cross product is done with vectors for finding normals for use in finding equations of planes (described later).
If only points are given the points need to be combined to create vectors for use in the cross product to get solutions.

Find angles with cross products:
|A × B| = |A||B|sin(@)

with right hand rule the dir() perpendicular line that is wanted always points "up" not "down"

dir() can help find volume by finding the n_^ (perpendicular vector) of the x and y vectors in 3d space
volume = |B*C|*(A*n_^) = |Y*Z|*(X*n_^) where n_^ is vector which is right angle formed from dir(X*Y)
n_^ can be found by cross product.
n_^ = B*C/|B*C| ?
n_^ = A.(B*C) ?
n_^ = det(A,B,C)