Question

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

Answer 1

`theta=33,4^o`

Explanation:

`step-1:" find C=A-B"`
`C=(A_x-B_x,A_y-B_y,A_z-B_z)=(6-1,-7+5,8+8)`
`C=(5,-2,16)`
`step-2:" find A.C (dot product)"`
`A*C=A_x*C_x+A_y*C_y+A_z*C_z=30+14+128=172`
`step-3:" find magnitude of A"`
`||A||=sqrt(6^2+7^2+8^2)=sqrt(36+49+64)=sqrt149`
`step-4:" find magnitude of C"`
`||C||=sqrt(5^2+2^2+16^2)=sqrt(25+4+256)=sqrt285`
`step-5:" use dot product formula"`
`A*C=||A||*||C||*cos theta`
`172=sqrt149*sqrt285*cos theta`
`cos theta=172/sqrt(149*285)`
`cos theta=0,8346678313`
`theta=33,4^o`