The position vectors of `A` and `B` are `2hat i+hat j-hat k` and `hat i+2hat j+3hat k` respectively. The position vector of the point which divides the line segment `AB` in the ratio `2:3` is

vec [AB]=3hat i+ hat j+ hat k and vec [CD]= -3hat i+2 hat j+4 hat k are two vectors. The position vectors of points A and C are 6 hat i+ 7 hat j+ 4 hat k and -9 hat j +2 hat k respectively. Find the position vector of point P on the line AB and point Q on the line CD such that vec [PQ] is perpendicular to vec [AB] and vec [CD] both.

If the position vectors of points A and B are 3hat(i)-2hat(j)+hat(k) and 2hat(i)+4hat(j)-3hat(k) respectively, then what is the length of vec(AB) ?

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection

The position vectors of the points A and B are 3hat i-hat j+7hat k and 4hat i-3hat j-hat k; find the magnitude and direction cosines of vec AB .

If the position vectors of the point A and B are 3hat(i)+hat(j)+2hat(k) and hat(i)-2hat(j)-4hat(k) respectively. Then the eqaution of the plane through B and perpendicular to AB is

If position vectors of two points A and B are 3hat(i)- 2hat(j) + hat(k) and 2hat(i) + 4hat(j) - 3hat(k) , respectively then length of vec(AB) is equal to?

The position vectors of the points A and B are 3hat i-hat j+7hat k and 4hat i-3hat j-hat k; find the magnitude and direction cosines of bar(AB)

The position vector of the points Pa n dQ are 5 hat i+7 hat j-2 hat k and -3 hat i+3 hat j+6 hat k , respectively. Vector vec A=3 hat i- hat j+ hat k passes through point P and vector vec B=-3 hat i+2 hat j+4 hat k passes through point Q . A third vector 2 hat i+7 hat j-5 hat k intersects vectors Aa n dBdot Find the position vectors of points of intersection.

The position vectors of points AandB w.r.t. the origin are vec a=hat i+3hat j-2hat k ,vec b=3hat i+hat j-2hat k respectively.Determine vector vec OP which bisects angle AOB, where P is a point on AB.

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are