If `P_1:vec r.vecn_1-d_1=0` `P_2:vec r.vec n_2-d_2=0` and `P_3:vec r.vecn_3-d_3=0` are three non-coplanar vectors, then three lines `P_1= 0`, `P_2=0`; `P_2=0`,`P_3=0` ; `P_3=0` `P_1=0` are

If P_(1):vec r*vec n_(1)-d_(1)=0P_(2):vec r*vec n_(2)-d_(2)=0 and P_(3):vec r*vec n_(3)-d_(3)=0 are three non- -d_(2)=0 coplanar vectors,then three lines P_(1)=0P_(2)=0;P_(2)=0,P_(3)=0;P_(3)=0P_(1)=0 are

If vec r=3vec p+4vec q and 2vec r=vec p-3vec q then

( If the planes )/(r*n_(1))=p_(1),vec r.n_(2)=p_(2) and vec r.n_(3)=p_(3), have a common line of intersection then

vec P+vec Q+vec R=0 and vec |p|=8,vec |Q|=15 and vec |R|=17 angle between vec P and vec Q is

For three vectors vec p,vec q and vec r if vec r=3vec p+4vec q and 2vec r=vec p-3vec q then

If vec p&vec s are not perpendicular to each other and vec r&vec &vec p=vec p xxvec p and vec r.vec s=0, then vec r=

If P(0, 1, 2), Q(4, -2, 1) and R(0, 0, 0) are three points, then anglePRQ is

Let vec r_1, vec r_2, vec r_3, , vec r_n be the position vectors of points P_1,P_2, P_3 ,P_n relative to the origin Odot If the vector equation a_1 vec r_1+a_2 vec r_2++a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a. a_1+a_2+dot+a_n=n b. a_1+a_2+dot+a_n=1 c. a_1+a_2+dot+a_n=0 d. a_1=a_2=a_3dot+a_n=0

Suppose that vec p, vec q and vec r are three non-coplanar vectors in R^3. Let the components of a vector vec s along vec p, vec q and vec r be 4, 3 and 5, respectively. If the components of this vector vec s along (-vec p+vec q +vec r), (vec p-vec q+vec r) and (-vec p-vec q+vec r) are x, y and z, respectively, then the value of 2vec x+vec y+vec z is