Prove that `(veca xx vecb)^2=|(veca.veca,veca.vecb),(veca.vecb,vecb.vecb)|`.

Show that (veca-vecb) xx(veca+vecb)=2(veca xx vecb)

Prove that [ veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

veca,vecb,vecc are three non zero vectors such that vecaxxvecb=vecc,vecbxxvecc=veca .Prove that veca,vecb,vecc are mutually at right angle and |vecb|=1,|vecc|=|veca| .

Hence, show that veca.vecb+vecb.vecc+vecc.veca=(-3)/2 if veca+vecb+vecc=0 .

Prove that (veca+vecb).(veca+vecb)=|veca|^2+|b|^2 if and only if veca,vecb are perpendicular, given veca!=vec0"and"vecb!=0 .

If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0 , find the value of veca.vecb+vecb.vecc+vecc.veca .

Consider the vectors veca=2i+j-2k and vecb=6i-3j+2k .Verify that abs(vecatimesvecb)^2=abs(veca)^2abs(vecb)^2-(veca.vecb)^2