Find the equation of the plane which passing through the points ` hati+ hatj+ hatk` and parallel to the plane `vecr.(2 hati-hatj+2 hatk)=5`

Find the equation of the plane which passing through the point hati + hatj + hatk and parallel to the plane vec r.(2hati - hatj + 2hatk) = 0.

Find the vector equation of a plane through the point hati+ hat j+hat k and parallel to the plane vecr.(2 hat i-hatj +2 hatk)=5 .

Find the vector equation of the line passing through the point (2,-3,1) and parallel to the planes vec r.(2hati-3hatj-hatk)=3 and vec r.(hati+hatj-hatk)=4 .

Find the vector equations of the plane passing through the points 3 hati+ 4 hatj+2 hatk, 2hati-2 hatj -hatk and 7 hati+6 hatk .

Find the equation of the plane passing through the line of intersection of the planes vec r.(hati+hatj+hatk)=1 and vec r.(2hati+3hatj-hatk)+4=0 and parallel to x-axis.

The vector equation of the line passing through the point (3, -1, 2) and parallel to the vector 2hati-3hatj+4hatk is -

Find the equation of the plane passing through the line of intersection of the plane vecr.(hati+3 hatj)+6=0 and vecr.(3 hati- hatj-4k)=0 which is at a unit distance from the origin.

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

Find the equation of a line passing through the point P(2,-1,3) and perpendicular to the lines vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vec r=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hati+hatj+5hatk)+lambda(3hati-hatj-5hatk) Also show that the plane contains the line vec r=(-hati+2hatj+5hatk)+lambda(hati-2hatj-5hatk) .