Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector `3hati+2hatj-2hatk`.

Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3hati+2hatj-8hatk .

i.Find the cartesian equation of the plane passing through the point (1,2,-3) and perpendicular to the vector 2hati-hatj+2hatk . ii. Find the angle between the above plane and the line (x-1)/2=(y-3)/3 =z/6 .

Find the vector and cartesian equation of the line through the point (3, -4, -2) and parallel to the vector 9hati+6hatj+2hatk .

Find the non parametric form of vector equation and the cartesian equation of the plane passing through the point (-1, 2, -3) and parallel to the lines vecr=(2hati-hatj+3hatk)+t(hati+hatj-2hatk) and vecr=(hati-hatj+3hatk)+s(3hati-hatj-2hatk)

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 and cartesian equation of the line through the point (1, 2, -2) and in parallel to (3hati-4hatj+5hatk) .

Find the vector and cartesian equations of the plane that passes through the point (1,0,-2) and normal to hati+hatj-hatk .

The vector equation of the plane through the point (2,1,-1) and parallel to the plane vecr.(hati+3hatj-hatk)=0 is

Find the vector and cartesian equations of the planes a. that passes through the point (1,0,-2) and normal to the planes is hati+hatj-hatk b. that passes through the point (1,4,6) and the normal vector to the plane is hati-2hatj+hatk .