Find the equation of the plane passing through (3, 4, -1), which is parallel to the plane `vecr*(2hati-3hatj+5hatk)+7=0`.

Find the equation of the plane through (3,4,-1) which is parallel to the plane vecr.(2hati-3hatj+5hatk)+7=0

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

Find the equation of the plane passing through (a,b,c) and parallel through plane vecr.(hati+hatj+hatk)=2 .

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

Write the vector equation of the plane passing through the point (a, b,c) and parallel to the plane vecr. (hati + hatj + hatk) = 2.

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

The equation of plane passing through the point hati+hatj+hatk and paralel to the plane vecr.(2hati-hatj+2hatk)=5 is

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 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.