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- Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1) Along The ff Paths In Space if straight lines from (0,0,0) to (1,0,0) then to (1,1,1)4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in thedirectiona. of vector v =<4,3> and toward the origin.
- If x and y are orthonormal vectors, then find the value of( ||x+y||^2) +(||x_y||^2)True or False and explain1- For any two non parallel and non orthogonal vectors a and b with angle θ between them, it holds that cosθ(a.b) = sinθ(axb). 2- Ifr(t)=⟨−4cos(2t),3sin(3t),ln(2t)⟩,then the ∫r(t)dt is equal to⟨−2sin(2t),−cos(3t),tlnt−t⟩+C,where C is a vector constant of integration.Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1) Along The ff Paths In Space if the straight line joining (0,0,0) and (1,1,1)
- Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and y2+z2=32y2+z2=32 at the point (−4,−4,4)(−4,−4,4).Compute the vector assigned to the pointP = (−3, 5) by the vectorfield:(a) F(x, y) = (xy,y − x)(b) F(x, y) = (4, 8)(c) F(x, y) = 3x+y , log2(x + y)find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8), direction vector v = (1, 0, 1)