If ` vec a , vec b , vec c`are three mutually perpendicular vectors of equalmagniltgude, prove that ` vec a+ vec b+ vec c`is equally inclined with vectors ` vec a , vec b , a n d vec cdot`also find the angle.

If ` vec a , vec b , vec c`are three mutually perpendicular vectors of

1.	If ` vec a , vec b , vec c`are three mutually perpendicular vectors of equalmagniltgude, prove that ` vec a+ vec b+ vec c`is equally inclined with vectors ` vec a , vec b , a n d vec cdot`also find the angle.
Answer» `abs(veca)=abs(vecb)=abs(vecc)=lamda` `vecavecb=vecbveccveccveca=0` `abs(veca+vecb+vecc)^2=(veca+vecb+vecc)(veca+vecb+vecc)` `=abs(veca)^2+0+0+abs(vecb)^2+abs(vecc)^2` `=lambda^2+lambda^2+lambda^2` `=3lambda^2` `abs(veca+vecb+vecc)=sqrt3lambda` `costheta_1=(veca(veca+vecb+vecc))/(abs(veca)abs(veca+vecb+vecc))=lambda^2/(lambdasqrt3lambda)=1/sqrt3=theta_1=cos^(-1)(1/sqrt3)` Similarly, `theta_1=theta_2=theta_3=cos^(-1)(1/sqrt3)`