What is the angle between #<1 , -2 , 7 > # and # < 7 , -2 , 2 > #?

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Answer 1 · 2016-11-10T06:27:08

The angle is #=63.2º#

The angle between two vectors is given by the dot product.

#vecu.vecv=∥vecu∥*∥vecv∥ costheta#
#theta# is the angle between the two vectors

Here #vecu.vecv=〈1,-2,7〉.〈7,-2,2〉=7+4+14=25#
The modulus of the vectors are :

#∥〈1,-2,7〉∥ = sqrt(1+4+49) = sqrt(54)#

#∥〈7,-2,2〉∥= sqrt(49+4+4)= sqrt57#

#costheta=vecu.vecv/(∥vecu∥*∥vecv∥)=25/(sqrt54*sqrt57)=0.45#

#theta=63.2º#