2.4 Cross Pm given that the velocity is 2: t 9.) Find the position function řit)...
Line Segment? -- + + ok -Pas-pa) .) to c leng of jlt) = <-sin (36), is 710) = 3i +25 +6K t (st?+1)4 given that the velocity is the initial position esty od Section 13.1 Parameterization 1. Uw the start point the point he cotire segment as the din 9.) Find the position fonction Adu PO Line Segment Section 12.2 Vector Component Form: - (s. 12.) or + 1) + wyk actor from PP. Papa) to .92.a): PO -...
Questions 1 and 2 1. Find the gradient of f(I, y) = sin(Zy+5). 2. Let f(x, y, z) - ryz + x) (a) Find the gradient of f. (b) Find an equation of the tangent plane to the level surface ryz + 2 = 5 at the point (2,1,1).
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) (4t, 2 sin(t), cos(2t)) 5(0) (0, 5,5) r(t) Preview Preview Preview The position of an object at time t is given by the parametric equations Find the horizontal velocity, the vertical velocity, and the speed at the moment wheret - 4. Do not worry about units in this problem. Horizontal Velocity - Preview Vertical Velocity- Preview Preview peed- Find the position vector for...
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...
please answer question 4-7 Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
for the curve r(t) find an equation for the indicated plane at the given value of t 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D) z -9 (3t sint+3 cos t)i + (3t cos t-3 sin t)j+ 4k; normal plane at t 1.5r.. A) y=-3 57) r(t) 57) B) y 3 C)x-y+z-3 D) x+y+z=-3 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D)...
A particle moves in the plane with position given by the vector valued function r(t)=cos^3(t)i+sin^3(t)j MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
Question 3. (15 pts) Given the function z = sin(ry) +2. Find the tangent plane equation at (1,0,2).
9. Find the velocity, acceleration, and speed of a particle with the given position function: a) r(t) = ti + taj + 2k, t = 1 b) r(t) = 3 costi + 2 sin tj, t = 3
Find the position function x(t) of a moving particle with the given acceleration a(t), initial position Xo = x(0), and initial velocity vo = v(O). a(t) = 4(t+3)2, v(0) = - 4, x(0) = 2