If #A = <1 ,6 ,-8 >#, #B = <-9 ,4 ,-8 ># and #C=A-B#, what is the angle between A and C?

Question

943 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-11T06:23:15

The angle is #=77.6º#

Let'scalculate #vecC=vecA-vecB=〈1,6,-8〉-〈-9,4,-8〉=〈10,2,0〉#

The angle is given by the dot product definition
#vecA.vecC=∥vecA∥*∥vecC∥costheta#
where #theta# is the angle between the two vector.

#vecA.vecC=〈1,6,-8〉.〈10,2,0〉=10+12-0=22#

The modulus of #vecA=∥〈1,6,-8〉∥=sqrt(1+36+64)=sqrt101#

The modulus of #vecC=∥〈10,2,0〉∥=sqrt(100+4)=sqrt104#

So, #costheta=22/(sqrt101*sqrt104)=0.214#

#theta=77.6º#