Find a vector parametric equation (t) for the linethrough the points P = (1, -4) and Q = (-2,-9).r(t)Find a vector parametric equation r(t) for the linethrough the points P = (4, 2, 3) and Q = (9, −2, −1)r(t)=r(t)=Find a vector parametric equation r(t) for the linethrough the points P = (–4, −4, −3) andQ = (0, −6, −2).=

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Answered: Find a vector parametric equation (t)…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.CR: Chapter Review

Problem 9CC

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VelocitySuppose that in Exercise 55 the current is flowing at 1.2 mi/hr due south. In what direction should the swimmer head in order to arrive at a landing point due east of his starting point? VelocityA river flows due south at 3mi/h. A swimmer attempting to cross the river heads due east swimming at 2mi/h relative to the water. Find the true velocity of the swimmer as a vector.
This is a two part problem. A. Find a vector parametric equation r(t) for the line through the points P = (0,2) and Q = (-4,0). B. Find a vector parametric equation r(t) for the line through the points P = (-5,-4,-4) and Q = (-10,-3,-2).
A) find a vector parallel to the line of intersection of the planes -3x - 2y - 2z = -1 and -4x - 2y + 4z = 6 B) show that the point (-1,1,1) lies on both planes. Then find a vector parametric equation for the line of intersection.
Find a vector equation and parametric equations for the line. (Use the parameter t.) the line through the point (7, 0, −3) and parallel to the line x = 4 − 2t, y = −1 + 3t, z = 6 + 6t
(a) Find a vector parallel to the line of intersection of the planes −4x − 2y + z = −7 and 5x +2y − 5z = 12v→ = (b) Show that the point ()(1, 1, −1) lies on both planes. Then find a vector parametric equation for the line of intersection. r→ =
Find parametric equations for the line that passes through the point P and is parallel to the vector v. (Enter your answers as a comma-separated list. Let x, y, and z be in terms of t.) P(3, 2, 1), v = 0, −4, 2
(A) Find the parametric equations for the line through the point P = (-2, 5, -3) that is perpendicular to the plane 3x−1y+2z=1.Use "t" as your variable, t = 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. x = y = z = (B) At what point Q does this line intersect the yz-plane? Q = ( , , )
1. Determine equation of the line in vector form, parametric form, symmetric form and scalar equation of the following given: a) The line through the points (7,-3,1) and (-2,1,4). b) The line through the point (1,-5,0) and parallel to the line given by r (t)=(8–3t,-10+9t,-1-t) c) The line through the point (1,-7, 14) and parallel to the line given by x = 6t, y =9, z = 8-16t /12 2. Determine the intersection point of the two lines or show that they do not intersect. a) The line passing through the points (0,-9,-1) and (1,6,-3) and the line given by F(t)=(-9-4t, 10+6t, 1–2t). b. The line given by x = 1+6t, y = -1–3t, z = 4+12t and the line given by x = 4+t, y = -10-8t, z=3-5t. c. The line given by r (t)=(14+5t, -3t, 1+7t) and the line given by r(t) =(3-3t, 5+2t, -2+4t). d. Does the line passing through (-5,4,-1) and (-3,-5,0) intersect the yz-plane? If so, give the point. e. Does the line given by r (t) =(6+t, -8+14t, 4t) intersect the xz-plane? If so, give the point. 3. Which of the…
Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(−4, −1, −1), Q(−1, −7, −3) r(t) = Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)
1. Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = 16-t2, e−2t, ln(t + 3) 2. Find a vector equation and parametric equations for the line segment that joins P to Q. P(3.5, −1.4, 3.1), Q(1.8, 0.3, 3.1) 3. At what points does the curve r(t) = t i + (5t − t2) k intersect the paraboloid z = x2 + y2?
Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q corresponds to t = 1.) P(−7, −5, −1), Q(−1, −9, −6) (a) r(t) = (b) Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)

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Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).