If ` vec b` is a vector whose initial point divides thejoin of `5 hat ia n d5 hat j` in the ratio `k :1` and whose terminal point is the origin and `| vec b|lt=sqrt(37),then k` lies in the interval a. `[-6,-1//6]` b. `(-oo,-6]uu[-1//6,oo)` c. `[0,6]` d. none of these

If vec b is a vector whose initial point divides thejoin of 5 hat ia n d5 hat j in the ratio k :1 and whose terminal point is the origin and | vec b|lt=sqrt(37),t h e nk lies in the interval

If vec b is a vector whose initial point divides the join of 5 hat i and 5 hat j in the ratio k :1 and whose terminal point is the origin and | vec b|lt=sqrt(37),then , k lies in the interval a. [-6,-1//6] b. (-oo,-6]uu[-1//6,oo) c. [0,6] d. none of these

Find a vector whose length is 3 and which is perpendicular to the vector vec a=3 hat i+ hat j-4 hat k\ a n d\ vec b=6 hat i+5 hat j-2 hat kdot

Find the angle between the vectors vec a\ a n d\ vec b where: vec a= hat i- hat j\ a n d\ vec b= hat j+ hat k

Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lambda hat ka n d2 hat i- hat j+lambda hat k , respectively. Vector hat i- hat j+6 hat k is perpendicular to the plane containing the origin and the points Pa n dQ . Then lambda equals a -1//2 b. 1//2 c. 1 d. none of these

Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lambda hat ka n d2 hat i- hat j+lambda hat k , respectively. Vector hat i- hat j+6 hat k is perpendicular to the plane containing the origin and the points Pa n dQ . Then lambda equals 1//2 b. 1//2 c. 1 d. none of these

If vec A=4 hat i+6 hat ja n d vec B=3 hat j+4 hat k , then find the component of vec AB

If | vec a|=2,\ | vec b|=7\ a n d\ vec axx vec b=3 hat i+2 hat j+6 hat k ,\ find the angle between vec a\ a n d\ vec bdot

Find the unit vector in the direction of vec a+ vec b ,\ if\ vec a=2 hat i- hat j+2 hat k\ a n d\ vec b=- hat i+ hat j- hat kdot

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