Question #82dbe

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Answer 1 · 2017-01-20T17:21:46

Given #absvec(a)=3;absvec(b)=4 and absvec(c)=5#

Again

#veca_|_(vecb+vecc) #

#=>veca.(vecb+vecc)=0.......[1]#

#vecb_|_(vecc+veca) #

#=>vecb.(vecc+veca)=0..........[2]#

#vecc_|_(veca+vecb) #

#=>vecc.(veca+vecb)=0............[3]#

Adding [1],[2] and [3] we get

#2(veca.vecb+vecb.vecc+vecc.veca)=0#

#=>2abs(veca.vecb+vecb.vecc+vecc.veca)=0#

Now
#abs(veca+vecb+vecc)^2=absveca^2+absvecb^2+absvecc^2+2abs(veca.vecb+vecb.vecc+vecc.veca)#

#=>abs(veca+vecb+vecc)^2=3^2+4^2+5^2+0#

#=>abs(veca+vecb+vecc)^2=50#

#=>abs(veca+vecb+vecc)=sqrt50=5sqrt2#