Find the equation of the line parallel to `2hati-hatj+3hatk` and passing through the point (5,-2,4)`

Find the vector equation of a line parallel to the vector 2hati-hatj+2hatk and passing through a point A with position vector 3hati+hatj-hatk .

The distance of the point 3hati+5hatk from the line parallel to 6hati+hatj-2hatk and passing through the point 8hati+3hatj+hatk is

Find the equation of the line (vector and Cartesian both) which is parallel to the vector 2hati-hatj+3hatk and which passes through the point (5,-2,4)

Find the vector equation of the line which is parallel to the vector 3hati-2hatj+6hatk and which passes through the point (1,-2,3) .

Find the vector equation of the plane passing through the point (1,1,1) and passing through the intersection of the planes vecr.(hati-hatj+3hatk)+1=0 and vecr.(2hati+hatj-hatk)-5=0 .

Find the equation of the line passing through point 2hati-hatj+3hatk and parallel to vector hati+hatj-2hatk in vector form as well as Cartesian form.

Find the equation of the line through the point hati+hatj-3hatk and perpendicular to the lines vecr=2hati-3hatj+s(2hati+hatj-3hatk)andvecr=3hati-5hatk+t(hati+hatj+hatk)

Find the vector equation of a plane which is parallel to the plane vecr.(2hati-hatj+2hatk)=5 and passes through the point whose position vector is (hati+hatj+hatk) .

Find the equation of the line in Cartesiasn form that passes through the point with positoin vector 2hati-hatj+4hatk and is in the direction hati+2hatj-hatk.

Find the equation of the plane through the point hati+4hatj-2hatk and perpendicular to the line of intersection of the planes vecr.(hati+hatj+hatk)=10 and vecr.(2hati-hatj+3hatk)=18.