given vectors a=(4,-2,3) and b= (0,3,-5) find
a./a/
b. axb
c the angle between a and b
d /axb/
a./a/ = a / |a| = (4/|a|,-2/|a|,3/|a|) where |a| = sqrt(4^2+(-2)^2+3^2) = sqrt(29)
axb = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1) = (6, 20, 18)
cos(theta) = (a.b) / (|a|*|b|) = (4*0) + (-2*3) + (3*(-5)) / (sqrt(29)*sqrt(34)) = -23 / (sqrt(29)*sqrt(34))
theta = arccos(-23 / (sqrt(29)*sqrt(34))) ≈ 133.11°
|axb| = sqrt(6^2+20^2+18^2) = sqrt(736) = 8sqrt(46)