Statement 1: In `"Delta"A B C , vec A B+ vec BC+ vec C A=0` Statement 2: If ` vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b`

If vec a and vec b are two vectors such that vec a + vec b is perpendicular to vec a - vec b ,then prove that |vec a| = |vec b| .

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

Prove that if the vectors vec a, vec b, vec c satisfy vec a+ vec b + vec c = vec 0 , then vec bxx vec c = vec c xx vec a = vec a xx vec b

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

Find |vec a| and |vec b| if (vec a + vec b).(vec a - vec b) = 3 and 2|vec b| = |vec a| .

Prove that vec a xx (vec b + vec c) + vec b xx(vec a + vec c)+ vec c xx(vec a + vec b) = vec 0

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

Show that for any three vectors veca , vec b and vec c [ vec a + vec b, vecb + vec c , vec c + vec a ] =2[vec a , vec b , vecc] .