Find a vector equation and parametric equations for the line. (Use the parameter t.)The line through the point (1, 0, 8) and perpendicular to the plane x + 4y + z = 5r(t) =(x(t), y(t), z(t))%3DNeed Help?Watch ItRead It

Given query is to find the the vector equation and the parametric equation for the line.

Answered: Find a vector equation and parametric…

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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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).
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
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Find parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to the vector 2j + k 2. The line through the point (3, -2, 1) parallel to the line x = 1 + 2t, y = 2 - t, z = 3t 3. The line through (1, 1, 1) parallel to the z-axis 4. The line through (2, 4, 5) perpendicular to the plane 3x + 7y - 5z = 21
Solve the following vector problems and parametric equations:a) Find the vector equation and the parametric equation of the straight line on R3 running throughpoint � "(2,1, −3) and parallel to the vector v = (3, −2, 4).b) Use the equation obtained in a) to find 2 points on the line,which is not point P0.c) Use the equation again obtained in a) to test what the point is� (11, −5,9) and point � (14, −3,17) lie on this line
Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, 0, 0), Q(1, 9, 3) We know that the vector equation for the line segment that joins the tip of r0 to the tip of r1 is r(t) = ( 1−t )r0 + 0 r1, for 0 ≤ t ≤ 1.
Find parametric equations for the lines in Exercises 1–4. 1. The line through the point P(3, -4, -1) parallel to the vector i + j + k 2. The line through P(1, 2, -1) and Q(-1, 0, 1) 3. The line through P(-2, 0, 3) and Q(3, 5, -2) 4. The line through P(1, 2, 0) and Q(1, 1, -1).
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Find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, P0(x0, y0, z0), and a vector n = <a, b, c> that is parallel to the line. Then the equation of the line is x − x0 = at, y − y0 = bt, z − z0 = ct.) z = e7(x)^2 + 2(y)^2, P(0, 0, 1)
a) Interpret the parametric equations x = x1+(x2-x1)t y = y+(y2-y1)t where 0<= t <=1, which the line segment joins the points P1(x1,y1) andP2(x2,y2) . b) Hence, find the parametric equations which represent the line segmentfrom (−2 , 7) to (3 , −1).

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Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (1,0, 8) and perpendicular to the plane x + 4y + z = 5 r(t) = (x(t), y(t), z(t)) %3D Need Help? Read It Watch It