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Answer 1 · 2017-07-17T06:50:02

The angle is #=2/3pi#

#veca# and #(veca+vecb)# are perpendicular

Therefore, the dot product is #=0#

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

#veca.veca=||veca||^2#

But,

#||veca||=1/2||vecb||#

The angle between #veca# and #vecb# is given by the dot product

#veca.vecb=||veca||*||vecb||costheta#

#costheta=(veca.vecb)/(||veca||*||vecb||)#

#=(-||veca||^2)/(2||veca||^2)#

Therefore,

#theta=2/3pi#