Line 1:х — 31- y= z - 84Line 2:X=-2ty=2+2tz=6+2t1.If the given lines intersect at a point, computethe acute angle between line 1 and line 2.2. Find the equation of a plane in point-normalform containing line 1 and the point P(-1, 0, 7).

To find the given questions when two lines Line1 and Line2 are given :-

Answered: Line 1: 1 - y = Z – 8 2 х — 3 4 Line 2:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1.) Graph the following points on a graph show x and y axis label each point on graph. A(1,1) B(3,3) C(5,5), D(-1,-1), E(-3,-3) 2.) Graph the following F(-1,1) G(-2,2), H(-3,3) I(-6,6) show x and y axis lable each point on graph. 3.) Plot both questions 1 and 2 on same graph label all points does the two lines intersect and identify that point. 4.) Calculate the slope and intercept of the graph 1 all work. 5.) Calculate the slope and intercept of the graph 2 all work.
Determine the relative position of the line and the plane. If the line and the plane intersect, give the exact coordinates of the point of intersection and the angle formed by the line and the plane (rounded to one decimal).(a) D1:1−x3=y−42=z+ 2 and Π1: 3x−5z+ 3 = 0.(b) D1:1−x3=y−42=z+ 2 and Π2: (x, y, z) = (3,5,−1) +s(−1,3,2) +t(2,1 ,1).
Find parametric equations of the line that satisfies the stated conditions. The line through (8, 5) that is parallel to 9 i-5j. O x = 8+9t, y = 5-5t O x = 8+8t, y = 5+5t O x = 8+5t, y = 9-5t O x = 9+9t, y = -5-5t O x = 9+8t, y = -5+5t
5. (a) (i) Find the equation of the plane II through the points (1, 1, 1), (1,3,2), and (2,2,0). (ii) Find the equation of the line I through the points (3, 3, −3) and (2, 4, −2). (iii) Find the point where I and II intersect. (iv) Find the angle between II and I (in radians to 1 decimal place). (b) Sketch the curve with polar equation r = sin(30), 0 ≤ 0 < 2π, plotting all the points with r both positive and negative and including explanations for your answer. Do we get any extra points if we allow negative r?
Pls help ASAP.
Q1. Find the equation of the plane determined by the lines : L₁: (x = -2+1, y = 21+ 3, 2=4-1), L₂: (x = 3-1, y=-21+4, z = 1), then find the distance between them.
Let I, be the line described by the Cartesian equations • X= 1 y-11=2(z-8) Let , be the line described by the Cartesian equations • X=1 • y-11 = z-8 Compute the distance between I and I,.

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Line 1: 1 - y = Z – 8 2 х — 3 4 Line 2: x=-2t y=2+2t z=6+2t 1.If the given lines intersect at a point, compute the acute angle between line 1 and line 2. 2. Find the equation of a plane in point-normal form containing line 1 and the point P(-1, 0, 7).