Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
unit normal to the surface
n
|
|
6 i 3 j
2 k
7
Equation of the tangent plane in vector form is ( r a).n 0
Where
r x i y j
z k,
a i 2 j
3k
ie
6(x 1) 3(y 2) 2(z 3) 0
i.e., 6x + 3y + 2z = 18
18. Find the angle between the surfaces xlogz = y 2 - 1 and x 2 y = 2 - z at the
point (1, 1, 1).
Suggested answer:
Let
2
1 x log z y
2 x 2 y z
1
log z i 2y j
x
z
k
2
2xy i x
2
j
k
( 1)
(1,1,1 )
2
j
k
( 2)
(1, 1, 1)
2 i j
k
The angle between the surfaces is the angle between 1
and 2.
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