Consider the set of eight vectors `V[ahati+bhatj+chatk:a,b,c in {1-1}]`. Three non-coplanar vectors cann be chosen from V in `2^(p)` ways, then p is

Consider th set of eight vectors V = {a hat(i) + b hat(j) + c hat(k): a, b, c in {-1, 1}} . Three non-coplanar vectors can be chosen from V in 2P ways Then p is

Compute the resultant of three coplanar vectors P, 2P and 3P inclined at 120^@ with one another.

Suppose that vec(p), vec(q) and vec(r) are three non-coplanar vectors in R. 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 2x + y + z is

If the vectors a hati + hatj + hatk , hati + b hatj + hatk and hati + hatj + chatk are coplanar where a ne 1 , b ne 1 , c ne 1 , prove that 1/(1-a)+1/(1+b)+1/(1-c) = 1 .

If a,b,c in N the number of points having position vector ahati+bhatj+chatk such that 6lea+b+cle10

If vec a , vec b ,a n d vec c be three non-coplanar vector and p,q,r constitute the reciprocal system of vectors, then (la+mb+nc).(lp+mq+nr). is equals 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)

If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc) is

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati + b_(2)hatj + b_(3)hatk and vecc=c_(1)hati +c_(2)hatj +c_(3)hatk be three non-zero vectors such that vecc is a unit vector perpendicular to both vectors, veca and vecb . If the angle between veca and vecb is pi//6 "then" |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|^(2) is equal to

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 planes and vec n_1, vec n_2 and vec n_3 are three non-coplanar vectors, then three lines P_1= P_2=0 ; P_2= P_3=0 ; P_3= P_1=0 are a. parallel lines b. coplanar lines c. coincident lines d. concurrent lines