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

Find the vector equation of the plane passing through the intersection of the planes vecr cdot (2hati+2hatj-3hatk) = 7, vecr cdot(2hati + 5hatj + 3hatk) = 9 and through the point (2, 1, 3)

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

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 (1, 2, 3) and perpendicular to the plane vecr cdot(hati+2hatj-5hatk) + 9 = 0

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 .

Find the equation of the plane which contains the line of intersection of the planes vecr cdot(hati+2hatj+3hatk) - 4 = 0 and vecr cdot (2hati + hatj - hatk) +5 = 0 and which is perpendicular to the plane vecr cdot (5hati+3hatj-6hatk) +8 =0

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