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

Find the equation of the line passing through the point with position vector hati-hatj+2hatk and perpendicular to the plane vecr.(2hati-hatj+3hatk)=5 .

Find the distance of the point with position vector -hati-5hatj-10hatk from the point of intersection of the line vecr=(2hati-hatj+2hatk)+lambda(3hati+4hatj+12hatk) and the plane vecr*(hati-hatj+hatk)=5 .

Find the work done by the force vecF=hati+2hatj+hatk acting on a particle, if the particle is displaced from the point with position vector 2hati+hatj+hatk to the point with position vector 3hati+2hatj+4hatk .

Find the image of the point hati+3hatj+4hatk in the plane vecr.(2hati-hatj+hatk)+3=0 .

Using vector method, show that the points whose position vectors are , 2hati-hatj+hatk and hati-3hatj-5hatk and 3hati-4hatj-4hatk form a right angled triangle.

Find the vector equation of a plane passing through the point having position vector 2hati+hatj+hatk and perpendicular to the vector: 4hati-2hatj+3hatk .

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

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) .