Express the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) * Express the vector field B = (x2 – y²)ay + xza, in spherical coordinates at ( 4, 30°, 120°) 6.78ar + 0.232ae + 9aØ -3.87ar - 0.332ae + 5aØ -9.87ar + 0.232ae + 6aØ -3.87ar + 0.232ae + aØ O O
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- A ball is thrown eastward into the air from the origin (in thedirection of the positive x-axis). The initial velocity is 50i+ 80k, with speedmeasured in feet per second. The spin of the ball results in a sounthwardacceleration of 4f t/s^2 , so the accelearation vector is a = −4j − 32k. Where does the ball land and with what speed?A stone is thrown from a rooftop at time t=0 seconds. Its position at time t is given by r(t)=6ti−4tj+(9.8−4.9t^2)k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north, and k points up.(a) How high is the rooftop? meters.(b) When does the stone hit the ground? seconds.(c) Where does the stone hit the ground? (in meters)(d) How fast is the stone moving when it hits the ground? (in meters per second)Consider the following points: A(1, 1, −2), B(−1, 2, 1) and C(1, 0, 1). Determine theparametric equations of either the unknown line or the unknown plane in R^3a. the line passing through the point B that is perpendicular to the vector→AB ×→AC
- . Assuming the +x-axis is horizontal to the right for the vectors in the following figure, find the following scalar products: (a) →A · →C ; (b) →A · →F; (c) →D · →C ; (d) →A · (→F + 2 →C); (e) ^i · →B; (f) ^j · →B; (e) (3 ^i − ^j) · →B, and (h) B^ · B→.Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector 4u - (2v - w)or scalar.The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(22t – sin(22t))i + 3(1 – cos(22t))} Find the velocity vector of the point. v(t) = (66 – 66 cos(22t) )i + 66 sin( 22t)jv Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = 66y cos( 22t) + sin( 22t) x
- A ball is thrown eastward into the air from the origin. The initial velocity is (50, 0, 80), with speed measured in feet per second. The spin of the ball results in a southward acceleration of 4 ft/s², so the acceleration vector is (0, -4,-32). Where does the ball land and with what speed?The position vector of a moving particle in space at time t is given by the vector function r (t) = - (5 - t)2i + (2t - 1) j + (5 - t)3/2 K Find the largest possible time when the particle reaches the speed of 4 units. Enter an integer or a fully reduced fraction such as 0, 15, 3/4 , etc. No Spaces Please.Vector A has a magnitude of 19.6 and is at an angle of 80.5° counterclockwise from the +x-axis. Vector B has a magnitude of 27.1 and is -40.3° from the +x-axis. Resolve Á and B into components, and express in ijk unit vector form, À = A‚i + A‚j %3D B = B,i + Bj where Ax, Ay, Bx, and By are the calculated values of the x- and y-components of vectors A and B, respectively. = Calculate the dot product between A and B. A• B = Calculate the angle 0 between A and B.
- Suppose the position of a particle in motion at time is given by the vector parametric equation r(t)=<4(t-2)^2,9,2t^3-6t^2 Find the speed of the particle at time tFind the time(s) when the particle is stationary. If there is more than one correct answer, enter your answers as a comma separated list.If r(t) = (1+ t)/?i +(1- t)/2j +tk, t= 0 then the binormal vector B is %3D 3' اخترأحد الخياراتVector v with initial point P = (x1, yı) and terminal point P, = (x2, y2) is equal to the vector v = ()i + (_j.