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Question 01: Sketch the vectors ro =< -1,2 > and v=< 1,1> and then sketch the six vectors ro ±v,r, ± 2v,r, ± 3v. Draw the line L:-1+t,y= 2+ t, and describe the relationship between L and the vectors you have sketched. What is the vector equation of L?

Question 01: Sketch the vectors ro =< -1,2 > and v=< 1,1> and then sketch the six vectors ro ±v,r, ± 2v,r, ± 3v. Draw the line L:-1+t,y= 2+ t, and describe the relationship between L and the vectors you have sketched. What is the vector equation of L?

Advanced Engineering Mathematics
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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Question 01: Sketch the vectors ro =< -1,2 > and v=< 1,1 > and then sketch the six vectors ro ±v,ro ± 2v,ro ± 3v. Draw the line L: –1+t,y = 2+ t, and describe the relationship between L and the vectors you have sketched. What is the vector equation of L? Question 02: Let L, and L2 be the line whose parametric equations are: L1:x = 4t, y = 1 – 2t, z = 2 + 2t L2:x = 1+ t, y = 1 – t, z = -1+ 4t • Show that L1 and L2 intersect at the point (2,0,3). • Find, to the nearest degree, the acute angle between L1 and L2 at their intersection. • Find parametric equations for the line that is perpendicular to L, and L2 and passes through their point of intersection.
Transcribed Image Text:Question 01: Sketch the vectors ro =< -1,2 > and v=< 1,1 > and then sketch the six vectors ro ±v,ro ± 2v,ro ± 3v. Draw the line L: –1+t,y = 2+ t, and describe the relationship between L and the vectors you have sketched. What is the vector equation of L? Question 02: Let L, and L2 be the line whose parametric equations are: L1:x = 4t, y = 1 – 2t, z = 2 + 2t L2:x = 1+ t, y = 1 – t, z = -1+ 4t • Show that L1 and L2 intersect at the point (2,0,3). • Find, to the nearest degree, the acute angle between L1 and L2 at their intersection. • Find parametric equations for the line that is perpendicular to L, and L2 and passes through their point of intersection.
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