Show that the points `(hati - hatj + 3 hatk ) and (hati+ hatj + hatk)` are equidistant from the plane `vecr. (5 hati + 2 hatj - 7 hatk ) + 9=0` and lies on opposite side of it.

Show that the points hati-hatj+3hatk and 3hati+3hatj+3hatk are equidistant from the plane r.(5i+2j-7k)+9=0 and are on the opposite sides of it.

The angle between the line vecr = ( 5 hati - hatj - 4 hatk ) + lamda ( 2 hati - hatj + hatk) and the plane vec r.( 3 hati - 4 hatj - hatk) + 5=0 is

Show that the line vecr=(2hati-2hatj+3hatk)+lambda(hati-hatj+4hatk) is parallel to the plane vecr.(hati+5hatj+hatk)=7 .

If the point of intersection of the line vecr = (hati + 2 hatj + 3 hatk ) + ( 2 hati + hatj+ 2hatk ) and the plane vecr (2 hati - 6 hatj + 3 hatk) + 5=0 lies on the plane vec r ( hati + 75 hatj + 60 hatk) -alpha =0, then 19 alpha + 17 is equal to :

Show that vector hati + 3hatj + hatk, 2 hati - hatj - hatk, 7 hatj + 3 hatk are parallel to same plane.

The position vectors of points A and B are hati - hatj + 3hatk and 3hati + 3hatj - hatk respectively. The equation of a plane is vecr cdot (5hati + 2hatj - 7hatk)= 0 The points A and B

Show that the line vecr=(4hati-7hatk)+lambda(4hati-2hatj+3hatk) is parallel to the plane vecr.(5hati+4hatj-4hatk)=7 .

Find the points of intersection of the line vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

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

Show that the three points -2hati+3hatj+5hatk, hati+2hatj+3hatk, 7hati-hatk are collinear