Consider the set of eight vector `V={a hat i+b hat j+c hat k ; a ,bc in {-1,1}}dot` Three non-coplanar vectors can be chosen from `V` is `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

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

Find the unit vector in the direction of the vector vec a= hat i+ hat j+ 2 hat k .

If the vector ahat i+ a hat j+ c hatk, hat i+hatk and chat i+c hat j+b hat k be coplanar, show that c^2= ab .

Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=hat i-hat j+hat k

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

Find the resultant of vectors vec a= hat i- hat j+2 hat k and vec b= hat i+2 hat j-4 hat kdot Find the unit vector in the direction of the resultant vector.

Statement 1: A component of vector vec b=4 hat i+2 hat j+3 hat k in the direction perpendicular to the direction of vector vec a= hat i+ hat j+ hat ki s hat i- hat jdot Statement 2: A component of vector in the direction of vec a= hat i+ hat j+ hat k is 2 hat i+2 hat j+2 hat kdot

Find the vector of length 3 unit which is perpendicular to hat i+ hat j+ hat k and lies in the plane of hat i+ hat j+ hat k and 2 hat i-3 hat j .