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

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 through the point (-3, 2, -4) and is parallel to the vector 3hati + 2hatj+ 4hatk .

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 equation of the plane passing through the point hati-hatj+hatk and perpendicular to the vectro 3hati-hatj-2hatk and show that the point 2hati+4hatj lies on the plane.

Find the equation of a line passes through the points whose position vectors are (hati+4hatj+hatk) and (2hati-hatj+5hatk) .

Find the equation of the plane through the point 2hati+3hatj-hatk and perpendicular to vector 3hati+3hatj+7hatk. Determine the perpendicular distance of this plane from the origin.

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

Find the angle between the vectors 4hati-2hatj+4hatk and 3hati-6hatj-2hatk.

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 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