What is the angle between #<1 , 5 , 3 > # and # < 4, 9 , 4 > #?

1 Answer
Mar 20, 2016

#alpha=14,07 ^o#

Explanation:

enter image source here
#"find dot product of <1,5,3> and <4,9,4> like animation above"#
#A.B=1*4+5*9+3*4#
#A.B=4+45+12#
#A.B=61#

#" now find the magnitude of A and B"#

#||A||=sqrt(1^2+5^2+3^2)=sqrt(1+25+9)=sqrt35#
#||B||=sqrt(4^2+9^2+4^2)=sqrt(16+81+16)=sqrt113#

#"Dot product is determined by:"#
#A.B=||A||*||B||*cos alpha#
#A*B=61#
#||A||=sqrt35#
#||B||=sqrt113#
#61=sqrt35*sqrt113*cos alpha#
#61=sqrt(35*113)*cos alpha#
#cos alpha=61/sqrt(35*113)#
#cos alpha=0,9699661782#
#alpha=14,07 ^o#