In the following cases, find the coordinates of the foot of the perpendicular
drawn from the origin (a)
2x + 3y + 4z – 12 = 0
(b)
3y + 4z – 6 = 0
(c)
x + y + z = 1
(d)
5y + 8 = 0
5 Find the vector and cartesian equations of the planes
(a)
that passes through the point (1, 0, – 2) and the normal to the plane is
ˆ
ˆ
ˆ i
j
k
+ −
(b)
that passes through the point (1,4, 6) and the normal vector to the plane is
ˆ
ˆ
2ˆ