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 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 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

If vec a= hat i- hat j\ a n d\ vec b=- hat j+ hat k find the projection of vec a\ on\ vec bdot

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

If vec a=4 hat i+3 hat j+ hat k\ a n d\ vec b= hat i-2 hat k\ t h e n\ fin d \ |2 vec bxx vec a|dot

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

Write a unit vector in the direction of the sum of the vectors vec a=2 hat i+2 hat j-5 hat k\ a n d\ vec b=2 hat i+ hat j-7 hat kdot

vec A B=3 hat i- hat j+ hat ka n d vec C D=-3 hat i+2 hat j+4 hat k are two vectors. The position vectors of the points Aa n dC are =6 hat i+7 hat j+4 hat ka n d=-9 hat j+2 hat k respectively. Find the position vector of a point P on the line A B and a point Q on the line C D such that vec P Q is perpendicular to vec A Ba n d vec C B both.

Write the position vector of a point dividing the line segment joining points A and B with position vectors vec a\ a n d\ vec b externally in the ration 1:4 where vec a=2 hat i+3 hat j+4 hat k\ a n d\ vec b=- hat i+ hat j+ hat kdot

Find vec adot vec b when: vec a= hat i-2 hat j+ hat k\ a n d\ vec b=4 hat i-4 hat j+7 hat k