Let us define the length of a vector `a hat i+b hat j+c hat ka s|a|+|b|+|c|dot` This definition coincides with the usual definition of length of a vector `a hat i+b hat j+c hat k` is and only if a. `a=b=c=0` b. any two of `a ,b ,a n dc` are zero c. any one of `a ,b ,a n dc` is zero d. `a+b+c=0`

If vec a = hat i + hat j, vec b = hat i + hat k, vec c = hat k + hat i, a unit vector parallel to vec a + vec b + vec c

If vec a= hat i+ hat j- hat k ,\ vec b=- hat i+2 hat j+2 hat k\ a n d\ vec c=- hat i+2 hat j- hat k , then a unit vector normal to the vectors a+b\ a n d\ b-c is hat i b. hat j c. hat k d. none of these

If vec a=hat i+hat j,vec b=hat j+hat k,vec c=hat k+hat i find the unit vector in the direction of vec a+vec b+vec c

let vec a=hat i+hat j-hat k and vec b=hat i-hat j-hat k and vec c be a unit vector perpendicular to vec a and coplanarwith vec a and vec b then vec c is

Let vec a=hat j-hat k and vec c=hat i-hat j-hat k. Then the vector b satisfying vec axvec b+vec c=0 and vec a*vec b=3, is

If vec a=hat i+hat j+hat k and vec b=hat j-hat k, find a vector vec c such that vec a x vec c=vec b and vec a*vec c=3

If hat a , hat b ,a n d hat c are three unit vectors, such that hat a+ hat b+ hat c is also a unit vector and theta_1,theta_2a n dtheta_3 are angles between the vectors hat a , hat b ; hat b , hat ca n d hat c , hat a respectively, then among theta_1,theta_2,a n dtheta_3dot a. all are acute angles b. all are right angles c. at least one is obtuse angle d. none of these

If vec a= hat i+ hat j+ hat k , vec c= hat j- hat k , vec adot vec b=3 and vec ax vec b= vec c , then vec b is equal to

If vec a=hat i+2hat j+hat k,vec b=2hat i+hat j and vec c=3hat i-4hat j-5hat k then find a unit vector perpendicular to both of the vector (vec a-vec b) and (vec c-vec b)