A line passes through two points whose position vectors `A(hat i+hat j-2hat k)` and `B(hat i-3hat j+hat k)`.Then the position vector of a point on it at a unit distance from A and closet to B

A line passes through the points whose position vectors are hat i+hat j-2hat k and hat i-3hat j+hat k the position vector of a point on the line at a unit distance from the first point is

Points A and B have position vectors (5hat i-2hat j+4hat k) and (hat i+3hat j-7hat k) then find |vec AB|

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

Find the image of the point with position vector (3hat i+hat j+2hat k) in the plane vec r*(2hat i-hat j+hat k)=4

Find the distance between the points A and B with position vectors hat i-hat j and 2hat i+hat j+2hat k.

Find the vector equation of the plane passing through three points with position vectors hat i+hat j-2hat k,hat i-hat j+hat k and hat i+2hat j+hat k .Also find the coordinates of the point of intersection of this plane and the line vec r=3hat i-hat j-hat k+lambda(2hat i-2hat j+hat k)

Find the vector equation of the plane passing through three points with position vectors hat i+hat j-2hat k2hat i-hat j+hat k and hat i+2hat j+hat k Also find the coordinates of the point of intersection of this plane and the line vec r=3hat i-hat j-hat k+lambda(2hat i-2hat j+hat k)

Distance between two points whose position vectors are 3hat i+hat j-2hat k and hat i-3hat j+5hat k is (a) 69units (b) sqrt(69) units (c) 13 units (d) 29 units

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

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