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10 Nov 2019

Linear Systems

Given these two lines:

1) y=3x+3

y=5/2x+2

Where do the two lines intersect?
Answers must be a point: (x, y)

Please show all work , so I can do it myself later.

Given these two lines:
Where do theh intersect?

2) y=3x+4
4x-2y=-4

Answers must be in a point: (x, y)

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Sixta Kovacek
Sixta KovacekLv2
5 May 2019

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Related questions

Linear systems

Graph these two lines

1) y=1x-3
y=5/2x+4

2) 5x-3y=9
-3x-3y=-15

Question1.

a)

Let L be the line containing thepoint P(2,-5,-1) and perpendicular to theplane 2x1+3x2+2x3=-3.

Find a vector equationfor L.

My answer: <2,-5,-1>+ t<2,3,2> (correct)

b)

At what pointdoes

Lintersect the yz-plane?

Question2:

x1 = -6 t - 4

x2 = - t+ 2

x3 = 5t - 6

and the second set ofparametric equations

x1 = 6t

x2 = ?

x3 = ?

describe the same line inR3. Find x2 and x3.

Question3:

It is one of 3 options foreach one: Parallel, perpindicular, or neither. Please explainwhy.

http://imgur.com/UbDuH8Z

Question4:

Find the point ofintersection of the two lines

a)

L1: x=1+t, y=-10-2t, z=-5-2t,

L2: x=7-4s, y=-10+2s, z=-7+3s.

Note that in general, twolines in 3D do not intersect. These two lines are carefully chosenso that they do

b)

Find the point where theline

x=1+2t,y=-4+t,z=-2-2t


intersects theplane

4x-y+3z=3.





Thanks. I have a lot ofpoints for this and will give it to someone that can helpme.

Let L be the line in parametric form x = s + 1, y = s - 2, z = 2s + 3, where s 2 R, and
let P and P' be the planes with cartesian equations 3x - 2y + z = 1 and x - y - 2z = 1,
respectively.
(a) Show that P and P' intersect in a line L' and find its parametric form.
(b) Determine the angle between the two planes P and P'.
(c) Show that the two lines L and L' are skew.
(d) Find points p on L and p' on L' such that the distance between them is minimised.
Hint: This will occur when the line from p' to p is perpendicular to both L and L'. The detailed answer to this part is especially crucial for me to understand as it asks to find points p and p' on lines L and L' r4spectively such that the distance is minimised, not find the distance as such.. I asked this question previously but wasnt satisfied with the answer.

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