Solve `a*r=x,b*r=y,c*r=z`, where a,b,c are givenn non-coplanar vectors.

Show that the vectors a-2b+4c,-2a+3b-6c and -b+2c are coplanar vector, where a,b,c are non-coplanar vectors.

p=2a-3b,q=a-2b+c and r=-3a+b+2c , where a,b,c being non-coplanar vectors, then the vector -2a+3b-c is equal to

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Let vec r=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a),w h e r e vec a , vec ba n d vec c are there non-coplanar vectors. It is given that vec r is perpendicular to vec a+ vec b+ vec c , the minimum value of x^2+y^2 is equal to (A) pi^2 (B) (pi^2)/4 (C) (5pi^2)/4 (D) none of these

If a,b and c be any three non-zero and non-coplanar vectors, then any vector r is equal to where, x=([rbc])/([abc]),y=([rca])/([abc]),z=([rab])/([abc])

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

If a, b and c are three non-coplanar vectors, then find the value of (a*(btimesc))/(ctimes(a*b))+(b*(ctimesa))/(c*(atimesb)) .

Let V be the volume of the parallelepiped formed by the vectors vec a = a_i hat i +a_2 hat j +a_3 hat k and vec b =b_1 hat i +b_2 hat j +b_3 hat k and vec c = c_1 hat i + c_2 hat j + c_3 hat k . If a_r, b_r and c_ r, where r = 1, 2, 3, are non-negative real numbers and sum_(r=1)^3(a_r+b_r+c_r)=3L show that V le L^3

If |{:((a-x)^(2),(a-y)^(2),(a-z)^(2)),((b-x)^(2),(b-y)^(2),(b-z)^(2)),((c-x)^(2),(c-y)^(2),(c-a)^(2)):}|=0 and vectors vecA, vecB and vecC , where vecA=a^(2)hati=ahatj+hatk etc. are non-coplanar, then prove that vectors vecX, vecYand vecZ " where " vecX =x^(2)hati+xhatj+hatk . etc.may be coplanar.