MTH622 Quiz by Lubna Mustafa

Name: MATH HELPER

Student ID: For Paid And Unique Solution ( )

Q01. Solution

First of all we calculate gradient of p y qy rz y

x

x z

(2pxy 2rzxy)

(2

(2pxy 2rzxy) p y qy rz y

i j k x y z

p y qy rz y i i x x

p y qy rz y j p q rz j y y

p y qy rz y k qyz r y k z z

i p q

x · x · z · x · x · z · x · x · x · x z · z · x · x · x · z · x · z

(2

the point (2,-1,3) the value of gradient is

=(-4p-12r)i+(4p+9q+12r)j+(-6q-4r)k

the maximum directional derivative parallel to x-axis if

as given magnitude of this maximum d rz j qyz r y k

at

x

x

irctional derivative is 72

so

-4p-12r

72. . . (1) along x-axis

4p+9q+12r

1. . . .(2) along y-axis

-6q-4r

1. . . (3) along z-axis

solving eq (1),(2)and (3)

we get the values of p,q an by

d r

p=-18

q

r