Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk
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- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}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).Determine the domain of the vector function r(t)=(t^2−4)/(t−2)i+sqrt(t+5)j+(e^t)* k Select one: a. [−5,2)∪(2,∞) b. [−5,∞) c. (−∞,∞) d. (−5,2)∪(2,∞) e. (−∞,2)∪(2,∞)
- Find the vectorequationof the line of intersection of the planes 2x-3y–z=5 and x+y+2z=1.A particle travels along curve C be described by vector function →r (t) =< 2t, 2t, 4 − t >. Find the distancethe particle travels from (2, 2, 3) to (4, 4, 2).Give an example of a linear combination that resulted in the zero vector that did NOT have 0's for the weights.
- 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 tangent to the curve of intersection of the two cyclinders x2 + y2 = 200 and y2 + z2 = 200 at the point (-10, –10, 10). (x2 + y? = 200 ve y2 + z2 = 200 silindirlerinin kesişimine (–10, –10, 10) noktasında teğet olan vektörü bulunuz.) Lütfen birini seçin: -400i + 400j + 400k O 400i+ 200j+ 400k O-200i+ 400j+ 400k O 400i+ 400j+ 200k O 300i+ 400j+ 400kFind a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i – j + 2k) (b)6(2i – j – 2k) (c) (21 - j- 2k) (d) 3(2i – j – 2k)
- The position of a particle is determined by the vector-valued function r(t)=<1-t^2, 3t, t^3>. Find the decomposition of the acceleration vector in terms of its tangential and normal components when the particle is at the point (0,3, 1).Find the vector parametrization r(t) of the line L that passes through the points (1, 1, 4) and (4, 4, 8). (Give your answer in the form (*, *, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) r(t) =Find a vector in the plane parallel to the line ax + by = c.
