A line passes through the point with position vector `2hati-hatj+4hatk` and is in the direction of `hati+hatj-2hatk`. Find the equations for the line in vector and in cartesian form.

A line passing through the point A with position vector veca=4hati+2hatj+2hatk is parllel to the vector vecb=2hati+3hatj+6hatk .Find the length of the perpendicular drawn on this line from a point P with position vector vecr_1=hati+2hatj+3hatk .

Find the vector equation of a line passing through the point with position vector (2hati-3hatj-5hatk) and perpendicular to the plane vecr*(6hati-3hatj-5hatk)+2=0 . Also, find the point of intersection of this line and the plane.

Write the projection of the vector 7hati+hatj+4hatk on the vector 2hati+6hatj+3hatk .

Find the projection of the vector hati+3hatj+7hatk on the vector 2hati-3hatj+6hatk .

Find the vector equation of the plane passing through three points with position vectors hati+hatj-2hatk, 2hati-hatj+hatk and hati+2hatj+hatk . Also find the co-ordinates of the point of intersection of this plane and the line vecr=3hati-hatj-hatk+lambda(2hati-2hatj+hatk) .

Find the vector equation of a line passing through the point with position vector hati-2hatj-3hatk and parallel to the line joining the points with position vectors hati-hatj+4hatk and 2hati+hatj+2hatk . Also find the cartesian form of the equation.

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2hati-hatj+4hatk and is in the direction hati + 2hatj - hatk

A line passes through the points whose position vectors are hati+hatj-2hatk and hati-3hatj+hatk . The position vector of a point on it at unit distance from the first point is (A) (1)/(5)(5hati+hatj-7hatk) (B) (1)/(5)(5hati+9hatj-13hatk) (C) (hati-4hatj+3hatk) (D) (1)/(5)(hati-4hatj+3hatk)

Find the distance of the point whose position vector is 2hati+hatj-hatk from the plane vecr.(hati-2hatj+4hatk)=9 .

The point having position vectors 2hati+3hatj+4hatk,3hati+4hatj+2hatk and 4hati+2hatj+3hatk are the vertices of