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12 terms

Randy - Linear Algebra

STUDY
PLAY
Add vectors v1 = <1, 4, -6>, v2 = <-3, 0, -2>
v1 + v2 = <1+ -3, 4 + 0, -6 + -2> = <-2, 4, -8>
Multiply by constant 2 * V1 = <1, 4, -6>
2 * V1 = <2, 8, -12>
Subtract vectors v1 = <1, 4, -6>, v2 = <-3, 0, -2>
v1 - v2 = <1- -3, 4 - 0, -6 - -2> = <4, 4, -4>
Dot Product
V * W = v1w1+ v2w2 + v3w3
Dot Product (Geometric)
V * W = |V||W| cos (Theda)
Dot Product (Geometric Understanding)
If Dot product is 0 then vectors are perpendicular
Dot Product (a*a)
|a|^2
Magnitude |a|
|a| = sqrt(a_x^2+a_y^2 + a_z^2)
Direction a
tan ^ -1 (a_x / a_y)
Cross Product
A x B = <AyBz - AzBy, AzBx - AxBz, AxBy - AyBx>
w = 7i + j - 3k
w = <7, 1, -3>
Cross Product
| V x W| = |V||w|sin (Theda)