Complete the empty spaces Starting from the point P, draw a path downhill in the

Question

Complete the empty spaces

Starting from the point P, draw a path downhill in the direction of the greatest change in altitude on the following contours of a hill. (Justify all features mentioned in class' 6. Given f(x,y) = x2 +y2. In the coordinate system above, sketch the gradient vector field Vl at the points (1, 0) and (1,2) only. (Justify all features) 7. Let T be the unit tangent vector of an oriented smooth curve C and F a vector field that has continuous component functions. The relation between Type I and Type II line integrals is given by where s is arc length 8. Let the tangent vector to a level curve C: f(x,y) -k at a point (x,^) be . Then the gradient vector

Explanation / Answer

8. tangent vector at a point (x,y) is perpendicular to gradient vector delta f of z.

6. f(x.y)= x^2 + y^2

delta (f) = (df/dx) + (df/dy)

so delta(f) = 2x + 2y ................. ( putting points in this equation we get delta (f) )

so now at point (1,0)

delta(f) = 2;

at point (1,2)....delta (f) = 6

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