Find the distane of the point `P(hati+hatj+hatk)` from the plane through the points `A(2hati+hatj+hatk)`, `B(hati+2hatj+hatk)` and `C(hati+hatj+2hatk)`

Show that the points : A(-2hati+3hatj+5hatk), B(hati+2hatj+3hatk) and C(7hati-hatk) are collinear.

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

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

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) .

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Find a unit vector in the direction of the resultant of the vectors (hati+2hatj+3hatk),(-hati+2hatj+hatk) and (3hati+hatj) .

Find the shortest distance between the lines vecr = (hati + 2hatj+hatk) + lambda(hati-hatj+hatk) and vecr = 2hati - hatj-hatk + mu(2hati+hatj+2hatk)

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 .

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.