I6-68. If~r 0 is center of sphere ,~r 1 is point on sphere where tangent plane is con-
structed and~ris a general point on the tangent plane, then the vector(~r−~r 1 )must
be perpendicular to the vector~r 1 −~r 0.I6-69.
∂F
∂x
=∂F
∂u∂u
∂x+∂F
∂v∂v
∂x
∂^2 F
∂x^2 =∂F
∂u∂^2 u
∂x^2 +∂u
∂x[
∂^2 F
∂u^2∂u
∂x+∂^2 F
∂u∂v∂v
∂x]+∂F∂v∂(^2) v
∂x^2 +
∂v
∂x
[
∂^2 F
∂v∂u
∂u
∂x+
∂^2 F
∂v^2
∂v
∂x
]
I6-70. (a) Use area of parallelogramA~×B~ so that the area of 1/2 of parallelogram
is^12 A~×B~.
I6-72. (b) 58
I6-74. (b) -12
Solutions Chapter 6