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 (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

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.

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

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 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 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 Cartesian equation of the plane passing through point A(1, 2, 3) and which is perpendicular to a vector vecn=2hati-3hatj+4hatk

Find the unit vector perpendicular to the plane vecr*(2hati+hatj+2hatk)=5 .

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