If A=<6,−7,8>, B=<1,−5,−8> and C=A−B, what is the angle between A and C?

1 Answer
ali ergin
Mar 14, 2016

θ=33,4o

Explanation:

step−1: find C=A-B
C=(Ax−Bx,Ay−By,Az−Bz)=(6−1,−7+5,8+8)
C=(5,−2,16)
step−2: find A.C (dot product)
A⋅C=Ax⋅Cx+Ay⋅Cy+Az⋅Cz=30+14+128=172
step−3: find magnitude of A
||A||=√62+72+82=√36+49+64=√149
step−4: find magnitude of C
||C||=√52+22+162=√25+4+256=√285
step−5: use dot product formula
A⋅C=||A||⋅||C||⋅cosθ
172=√149⋅√285⋅cosθ
cosθ=172√149⋅285
cosθ=0,8346678313
θ=33,4o

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