(a) Find symmetric equations for the line that passes through the point (1,-1, 7) and is parallel to the vector (-1, 3,-4).Ox+1_Y-1 2+-43Ⓒx-1-x+1-2-7-4Ox+1=X+¹=2=73-407(x-1)=3(y + 1) = -4(²-O(x+1)=3(x-1)=-4(2 +7).(b) Find the points in which the required line in part (a) intersects the coordinate planes.point of intersection with xy-planepoint of intersection with yz-planepoint of intersection with xz-plane

(a) Symmetric equation of a plane passing through a, b, c and having direction cosines l, m and n,…

Answered: (a) Find symmetric equations for the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 49EQ

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(-3,4) and (2,7) Find a vector equation of the line through the given pair of points and parametric equations of the line through the given pair of points.
Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through A(4, –1) and is perpendicular to the line through points M( –4, 3) and N(2,0). Can you please solve this with a full explanation, thank you!
1. Find a vector equation of the plane containing the points ?(2, 0, −1), ?(3, 4, 0), and ?(4, −1, 1).
Solve the problem. 1. Find the symmetric equations for the line through the point P(5, -3, -5) parallel to ther vector -6i +7j -7k.
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…
Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)
3. (a) Find the terminal point of the vector that is equivalent to u = (2, 3) and whose initial point is A(2,2).
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A = 0 1 −2 1 −1 4 5 0 0 1 3 1 the preimage of (0, 0, 0) (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)
Find the vector, parametric, and symmetric equations of the line which passesthrough the points A = (3, 1, −1) and B = (7, 0, 1).
14.1 Find the equation of the plane that is parallel to the vectors 3,0,2 and 0,1,3, passing through the point (4,0,−1). The equation of the plane is = (Type an equation using x, y, and z as the variables.)
1.Find the components of the vector whose initial point is (2, 3) and terminal point at (-3, 3).2.Let u = (1, 0, -2) and v = (2, -1, 0). Find the components of -3(u - 2v)3.If the norm of u is 2, the norm of v is 1 and the dot product of u and v is 4, then the angle between u and v is

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