Prove that
`axx(bxxc)+bxx(cxxa)+cxx(axxb)=0`

p,q and r are three vectors defined by p=axx(b+c),q=bxx(c+a) and r=cxx(a+b) Statement I: p,q and r are coplanar. Statement II: Vectors p,q,r are linearly independent.

Prove that |axxb^2 =a^2b^2 - (a.b)^2

The number of all 3-digit numbers abc (in base 10)for which (axxbxxc)+(axxb)+(bxxc)+(cxxa)+a+b+c=29 is

For any A sets A, B, C and D, prove that: (AxxB) nn (CxxD)=(A nnC)xx(BnnD)

Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec axx vec b)xx( vec cxx vec d)=0. Let P_1a n dP_2 be planes determined by the pair of vectors vec a , vec b ,a n d vec c , vec d , respectively. Then the angle between P_1a n dP_2 is a.0 b. pi//4 c. pi//3 d. pi//2

sube B, then prove that AxxA sube (AxxB) nn (BxxA).

Express the following in exponential form. axx axx bxx bxx cxxc xxd

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'veab' and vecc' be its reciprocal set. prove that veca=(b'xxc')/([veca'vecb'vecc']),vecb=(c'xxa')/([veca'vecb'vecc'])andvecc=(a'xxb')/([veca'vecb'vecc'])

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'veab' and vecc' be its reciprocal set. prove that veca=(b'xxc')/([veca'vecb'vecc']),vecb=(c'xxa')/([veca'vecb'vecc'])andvecc=(a'xxb')/([veca'vecb'vecc'])