What is the angle between #<1 , 3 , -4 > # and # < 5 , -2 , 2 > #?

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Answer 1 · 2016-10-02T17:18:16

#theta ~~ 1.833 radians#

Let #bar A = <1, 3, -4>#
Let #bar B = <5, -2, 2>#

#bar A•bar B = (1)(5) + (3)(-2) + (-4)(2)#

#bar A•bar B = -9#

#|barA| = sqrt(1² + 3² + (-4)²)#

#|barA| = sqrt26#

#|barB| = sqrt(5²+ (-2)² + 2²)#

#|barB| = sqrt33#

#bar A•bar B = |barA||barB|cos(theta)# where #theta# is the angle between the vectors

Substitute the known values and then solve for #theta#:

#-9 = sqrt26sqrt33cos(theta)#

#theta = cos^-1(-9/(sqrt26sqrt33))#

#theta ~~ 1.833 radians#