Let ` vec a , vec b ,a n d vec c` be non-coplanar unit vectors, equally inclined to one another at an angle`theta` then `[ veca vecb vecc ]` in terms of θ is equal to :

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is perpendicular to veca xx (vecb xx vecc) , then the value of [ veca xx ( vecb xx vecc)] xx vecc is equal to

i. If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3veca -7vecb -4 vecc ,3 veca -2vecb + vecc and veca + vecb +2 vecc are coplanar.

Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and the unit vector vec c is inclined at an angle theta to both vec aa n d vec bdot If vec c=m vec a+n vec b+p( vec axx vec b),(m ,n , p in R), then a. -pi/4lt=thetalt=pi/4 b. pi/4lt=thetalt=(3pi)/4 c. 0lt=thetalt=pi/4 d. 0lt=thetalt=(3pi)/4

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

If vec a , vec b , and vec c are mutually perpendicular vectors of equal magnitudes, then find the angle between vectors vec a and vec a+ vec b+ vec c dot

Let vec a, vec b, and vec c be three non coplanar unit vectors such that the angle between every pair of them is pi/3 . If vec a xx vec b+ vecb xx vec c=p vec a + q vec b + r vec c where p,q,r are scalars then the value of (p^2+2q^2+r^2)/(q^2) is

If vec a \ a n d \ vec b are two non-collinear unit vector, and ∣ ​ veca + vecb ∣ ​ = 3 ​ then (2 veca −5 vecb ).(3 veca + vecb ) =

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

If veca , vecb , vecc and vecd are four non-coplanar unit vectors such that vecd makes equal angles with all the three vectors veca, vecb, vecc then prove that [vecd vecavecb]=[vecd veccvecb]=[vecd veccveca]