Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.
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- Find a vector in the plane parallel to the line ax + by = c.A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set of parametric equations.
- Find a nonzero vector parallel to the line of intersection of the two planes 4x-2y+z=-1 and 5y-x-3z=-2 .Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the equation r1(t)=r2(t) may not produce all the points where the graphs of these functions intersect. Please Provide Unique Answer. Thank you!Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2x + 2z = 1 r = ( ,0 ) + t(-4, 8 ).
- Find the vector parametrization r(t) of the line L that passes through the points (4, 1, 2) and (9, 3, 7). (Give your answer in the form (*, *, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) r(t) =Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y, x). F(1, 1) = F(-3, -3) -Express the vector = + y. F 10 as a linear combination of -[-] and ÿ==