Let C be the straight path from 0 0 to 2 2 and let F rightar

Let C be the straight path from (0, 0) to (2, 2) and let F rightarrow = (y - x - 2)i rightarrow + (sin(y - x) - 2)j rightarrow. At each point of C, what angle does F rightarrow make with a tangent vector to C? angle = (Given your answer in radians.) Find the magnitude ||F rightarrow || at each point of C. ||F rightarrow || = Evaluate F rightarrow . dr rightarrow. F rightarrow . dr rightarrow =

Solution

vector c= 2i+2j
at point 0,0 vector f=-2i-2j
cos(theta)=u*v/|u|*|v|
cos(theta)=-8/8
theta=

same angle at point 2,2

b.)|f|=2*2 at each point of c

c.)int vector f and vercot dr

intigration (y-x-2)i+(sin(y-x)-2)j dx dy

x 0 to 2 and y 0 to 2

after sloveing intigration

we got =-8i+(sin(2)-8)j