If A=<4,−9,5>, B=<1,−3,−8> and C=A−B, what is the angle between A and C?

1 Answer
Bdub
Mar 4, 2016

C=<3,−6,13>→cosθ=<4,−9,5>⋅<3,−6,13>√42+(−9)2+52√32+(−6)2+132
cosθ=12+54+65(√122)(√214)→θ=cos−1(131√26108)=35.83∘

Explanation:

First find the vector C by subtracting vector B from vector . That is
C=<4−1,−9−(−3),5−(−8)>=<3,−6,13> Then find the dot product between vector A and C which is A⋅C=4(3)+(−9)(−6)+(5)(13). And divide that by the magnitude of both vector A and C and then take the cosine inverse to find the angle

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