pt) Match each of the curves described with one of the parametric equations, wit
ID: 2882971 • Letter: P
Question
pt) Match each of the curves described with one of the parametric equations, with 0 S t S 1 1. The ne segment from the origin to the point (-3,5 5.-5 r 2. The line segment from the point (0,4,0) on the y axis to the point (0,0, 1) on the 2-axis r 3. A parabolic curve from the point (0,-5,0) to the point (0,5,0) r 4. A semicircular arc of radius 2 in the za-plane traversed clockwise as viewed from (0, -1,0) 5. The ellipse with center at the origin, with one axis along th y axis, the other along the 2-axis; the axes have lengths 2 and 11 respectively. The ellipse is traversed in the counterclockwise direction when viewed from (1,0, 0, r 6. The line segment from the point (0,1,0) on the y-axis to the point (0,5,0) on the same axis. 7. The line segment from the point (-1,3, -1) to the point (-1, 3, 1 8. curve given by the line segment from the point (0,2,0) on the axis to the point (0,0, -4) on the 2-axis, followed by The the line segment to the point (4,0,0) on the ar-axis.Explanation / Answer
From the given question,
(1) Line segment from origin(0,0,0) to (-3,5,-5)
parametric form (x-0)/(-3-0) = (y-0)/(5-0) = (z-0)/(-5-0) =t
x= -3t
y=5t
z=-5t
xi + yj +zk
=-3ti + 5tj -5tk
option (L)
(2)Line segment from (0,4,0) to (0,0,1)
parametric form (x-0)/(0-0) = (y-4)/(0-4) = (z-0)/(1-0) =t
x= 0
y=-4t+4
z=t
x=0, yj +zk
= (-4t+4)j +(t)k
=(4-4t)j + tk
option (G)
(6)Line segment from (0,1,0) to (0,5,0)
parametric form (x-0)/(0-0) = (y-1)/(5-1) = (z-0)/(0-0) =t
x= 0
y=4t+1
z=0
x=0, yj , z=0
= (1+4t)j
option (C)
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