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

1 Answer
Mar 14, 2016

#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#