3 Find the Cartesian equation of the following planes:
(a)
ˆ
ˆ
ˆ
(
)
2
r
i
j
k
⋅
+
−
=
r
(b)
ˆ
ˆ
ˆ
(2
3
4 )
1
r
i
j
k
⋅
+
−
=
r
(c)
ˆ
ˆ
ˆ
[(
2 )
(3
)
(2
)
]
15
r
s
t i
t
j
s
t k
⋅
−
+
−
+
+
=
r
4 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