Prove that `( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)` and interpret it geometrically.

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

Prove that: ( vec a- vec b)*{( vec b- vec c)xx(vec c- vec a)}"=0

For any two vectors vec a and vec b , prove that: | vec a+ vec b|^2=| vec a|^2+| vec b|^2+2 vec adot vec b , | vec a- vec b|^2=| vec a|^2+| vec b|^2-2 vec adot vec b , | vec a+ vec b|^2+| vec a- vec b|^2=2(| vec a|^2+| vec b|^2) and | vec a+ vec b|^2=| vec a- vec b|^2 iff vec a_|_ vec bdot Interpret the result geometrically.

Prove that ( vec(A) + vec(B)) xx ( vec(A) - vec(B)) = 2 (vec(B) xx vec(A))

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

If vec a and vec b are unequal unit vectors such that ( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b , then angle theta between vec aa n d vec b is 0 b. pi//2 c. pi//4 d. pi

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c and vec a is not a zero vector. Show that vec b= vec c dot

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec a.vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec b.vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec c. vec d)/([ vec a vec b vec c])( vec axx vec b)