Write the vector equations of the plane throught the point (a,b,c) and parallel to the plane `vecr.(hati+hatj+hatk)=2`.

Find the vector equation of the line passing through the point (1,2,1) and perpendicular to the plane vecr.(2hati-hatj+hatk)=10 . Find the point of intersection of this line and the plane.

Find the equation of the plane passing through (a, b, c) and parallel to the plane vecr cdot(hati + hatj + hatk) = 2

Find the vector equation of the line passing through the point (3,1,2) and perpendicular to the plane vecr*2hati-hatj+hatk)=4 . Also find the point of intersection of this line and the plane.

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6.

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

Find the vector equation of the line through the origin, which is perpendicular to the plane vecr*(hati-2hatj+hatk)=3 .

Find the vector equation of the line through (4,3,-1) and parallel to the line: vecr=(2hati-hatj+3hatk)+lambda(3hati-hatj+4hatk)

Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk) =6 and vecr.(2hati+3hatj+4hatk)=-5 and point (1,1,1)

Find the vector equation of the plane passing through the intersection of the planes : vecr*(2hati-hatj+2hatk)=2 and vecr*(3hati+hatj-2hatk)=-2 and perpendicular to the veca=5hati-2hatj+3hatk .