If `vecp xx vecq = vecm xx vec n ` and `vecp xx vec m = vecq xx vecn`, show that `vecp- vecn` is parallel to `vecq - vecm` where `vecp ne vecn` and `vecq ne vecm`.

If vec (a) xx vec(b) = vec (c ) xx vec(d) and vec (a) xx vec ( c) = vec (b) xx vec (d ) , show that vec(a) - vec (d) is parallel vec(b) - vec (c) , where to vec (a) != vec (d) and vec ( b) != vec (c )

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) a. [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

Vectors vecm, vecn, vecr are such that vecm + vecn + vecr = 0 , prove that vecm xx vecn = vecn xx vecr = vecr xx vecm

If vecP . vecQ =IvecP X vecQI the angle between vecP and vecQ is.

If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove that (vecbxx(veca xx vecb))/(vecb.vecb)=vecq

The equation of a line passing through the point vec a parallel to the plane vec r. vec n=q and perpendicular to the line vec r= vec b+t vec c is a. vec r= vec a+lambda( vec nxx vec c) b. ( vec r- vec a)xx( vec nxx vec c) c. vec r= vec b+lambda( vec nxx vec c) d. none of these

Suppose that vec p,vecqand vecr are three non- coplaner in R^(3) ,Let the components of a vector vecs along vecp , vec q and vecr be 4,3, and 5, respectively , if the components this vector vec s along (-vecp+vec q +vecr),(vecp-vecq+vecr) and (-vecp-vecq+vecr) are x, y and z , respectively , then the value of 2x+y+z is

if veca xx vecb = vecc ,vecb xx vecc = veca , " where " vecc ne vec0 then (a) |veca|= |vecc| (b) |veca|= |vecb| (c) |vecb|=1 (d) |veca|=|vecb|= |vecc|=1

If vecP+vecQ=vecR and |vecP|=|vecQ|=sqrt(3) and |vecR|=3 , then the angle between vecP and vecQ is