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Answer 1 · 2017-11-10T08:38:21

#a=0, 4#

we will use the scalar (dot) product .

for two vectors

#veca=a_1hati+a_2hatj+a_3hatk," "vecb=b_1hati+b_2hatj+b_3hatk#

#veca*vecb=|veca||vecb|costheta----(1)#

#theta=#angle between the vectors

and can be be calculated by

#veca*vecb=a_1b_1+a_2b_2+a_3b_3---(2)#

we have

#vecv=ahati+hatj+hatk#

#vecw=hati+ahatj+hatk#

#theta=pi/3#

#|v|=sqrt(a^2+1+1)=sqrt(a^2+2#

#|vecw|=sqrt(1+a^2+1)=sqrt(a^2+2)#

using #(1)" & " (2)#

#|veca||vecb|costheta=veca*vecb=a_1b_1+a_2b_2+a_3b_3#

we have

#sqrt(a^2+2)sqrt(a^2+2)cos(pi/3)=(ahati+hatj+hatk)*(hati+ahatj+hatk)#

#(a^2+2)xx1/2=axx1+1xxa+1#

#1/2(a^2+2)=2a+1#

#a^2+2=4a+2#

#=>a^2-4a=0#

#a(a-4)=0#

either

#a=0" "#

#a=4#