How do you find the angle between u=<-1,9> and v=<3,12>?

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Answer 1 · 2016-11-18T18:12:49

The angle between, #theta = cos^-1((baru*barv)/(|baru||barv|)) ~~ 1.5 " radians"#

Given: #baru = <-1, 9> and barv = <3, 12>#

Compute the dot-product:

#baru*barv = (-1)(3) + (9)(12) = 105#

Compute the magnitude of #baru#:

#|baru| = sqrt((-1)^2 + 9^2) = sqrt(82)#

Compute the magnitude of #barv#:

#|barv| = sqrt(3^2 + 12^2) = sqrt(153)#

Another equation for the dot-product is:

#baru*barv = |baru||barv|cos(theta)#

Solve for #theta#:

#theta = cos^-1((baru*barv)/(|baru||barv|))#

Substitute in the computed values:

#theta = cos^-1((105)/(sqrt(82)sqrt(153))) ~~ 1.5 " radians"#