Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane `vecr cdot(hati+2hatj-5hatk) + 9 = 0`

Find the vector equation of the line passing through the point (1,2,1) and perpendicular to the plane vecr.(2hati-hatj+hatk)=10 . Find the point of intersection of this line and the plane.

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

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

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

Find the vector equation of the line through the origin, which is perpendicular to the plane vecr*(hati-2hatj+hatk)=3 .

Find the equation of the line passing through the point (1,-2,3) and perpendicular to the lines : vecr=(hati-2hatj+hatk)+lambda(hati+hatj+hatk) and vecr=(hati-hatj+2hatk)+mu(3hati-2hatj-5hatk)

Find the equation of the line passing through the point (1,2,-3) and perpendicular to the lines : vecr=(2hati-hatj-hatk)+lambda(2hati-hatj-3hatk) and vecr=(3hati-hatj-2hatk)+mu(hati+hatj+hatk)

Find the equation of the line passing through the point (2, -1, 3) and perpendicular to the lines : vecr=(hati-hatj+hatk)+lambda(2hati+hatj-3hatk) and vecr=(hati+hatj-hatk)+mu(hati+hatj+hatk)

Find the vector equation of the plane passing through the intersection of the planes vecr cdot (2hati+2hatj-3hatk) = 7, vecr cdot(2hati + 5hatj + 3hatk) = 9 and through the point (2, 1, 3)