Write the vector equation of the line passing through `(1,2,3)` and perpendicular to the plane ` vec r.( hat i+2 hat j-5 hat k)+9=0.`

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

Equation of the line passing through i+j -3k and perpendicular to the plane 2x - 4y + 3z + 5 =0 is -

Find the Cartesian equation of the plane passing through the point (1,2,-3) perpendicular to the vector2i-j+2k .

Find the vector equation of the Plane Passing through the intersection of the planes barr.(i+j+k)=6 and barr.(2i+3j+4k)=-5 and through the point (1,1,1).

Consider a plane passing through the point (5,2,-4) and perpendicular to the line barr=(i+j)+lambda(2i+3j-k) Write the equation in Cartesian form.

A plane is at a distance of 5 units from the origin and perpendicular to the vector 2hat(i) + hat(j) + 2hat(k) . The equation of the plane is a) vec(r ).(2hat(i) + hat(j) -2hat(k))=15 b) vec(r ).(2hat(i)+ hat(j)-hat(k))=15 c) vec(r ).(2hat(i) + hat(j)+ 2hat(k))=15 d) vec(r ).(hat(i) + hat(j) + 2hat(k))=15

Find a vector of magnitude 6 and perpendicular to both vec(a) = 2hat(i) + 2hat(j) + hat(k) and vec(b) = hat(i) - 2hat(j) + 2hat(k)

The straight line r = (hat(i) + hat(j) + 2hat(k)) + t(2hat(i) + 5hat(j) + 3hat(k)) is parallel to the plane r.(2hat(i) + hat(j) - 3hat(k)) = 5 . Find distance between the straight line and plane

The distance between the line vec(r) = (2hat(i) + 2hat(j) - hat(k)) + lambda(2hat(i) + hat(j) - 2hat(k)) and the plane vec(r).(hat(i) + 2hat(j) + 2hat(k)) = 10 is equal to