Find the vector equation of line passing through the point (-1, 2, 1) and parallel to the line `vecr=2hati+3hatj-hatk+lamda(hati-2hatj+hatk)` . Also , find the distance between these lines .

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 o 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 equation of a line passing through the point (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

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

Find the vector equation of a line passes through the point hati+3hatj+hatk and parallel to vector 3hati-2hatj+k .

Find the point where line which passes through point (1, 2, 3) and is parallel to line vecr=hati-hatj+2hatk+lamda(hati-2hatj+3hatk) meets the xy -plane.

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

Find the equation of a line passing through the point (2hati-3hatj-5hatk) and perpendicular to the plane vecr.(6hati-3hatj+5hatk) +2=0 . Also find the point of intersection of this line and the plane.

Findthe vector equation of a straighat line which passes through the points whose position vector are hati-2hatj+hatk and 3hatk-2hatj.

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