Let L1 be the line passing through the point P1=(−3, −1, 1) with direction vector →d1=[1, −2, −1]T, and let L2 be the line passing through the...

Let L₁ be the line passing through the point P₁=(−3, −1, 1) with direction vector →d₁=[1, −2, −1]^T, and let L₂ be the line passing through the point P₂=(8, −3, 1) with direction vector →d₂=[−1, 0, 2]^T.
Find the shortest distance d between these two lines, and find a point Q₁ on L₁ and a point Q₂ on L₂ so that d(Q₁,Q₂) = d. Use the square root symbol '√' where needed to give an exact value for your answer.

d =

Q₁ =
Q₂ =

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Let L1 be the line passing through the point P1=(−1, −2, −4) with direction vector →d=[1,...

Let L1 be the line passing through the point P1=(−1, −2, −4) with direction vector →d=[1, 1, 1]T, and let L2 be the line passing through the point P2=(−2, 4, −1) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1,Q2) = d. Use the square root symbol '√' where needed to give an exact value for your answer.

Let L be the line passing through the point P=(−3, −4, 2) with direction vector →d=[−3,...

Let L be the line passing through the point P=(−3, −4, 2) with direction vector →d=[−3, 3, 0]T. Find the shortest distance d from the point P0=(1, −5, −1) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where needed to give an exact value for your answer. d = 0 Q = (0, 0, 0)

Calculate the vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is:

Calculate the vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6).

1-: ?(?) = ln (3 − √2? + 1) ? ′(0) =? 2-Passing through the point...

1-: ?(?) = ln (3 − √2? + 1) ? ′(0) =? 2-Passing through the point x = 1 and ? = 2? Perpendicular to the straight line tangent to 3 + 5? - 2 parabola what is the equation of the normal?

Suppose that Line 1 contains the point P1 = (1,2,3) and the vector V1 = <2,1,-2>...

Suppose that Line 1 contains the point P1 = (1,2,3) and the vector V1 = <2,1,-2> is parallel to Line 1, and also that Line 2 contains the point P2 = (4,0,9) and that the vector V2 = <-2,-1,2> is parallel to line 2. Find the distance between Line 1 and Line 2.

1. a.) determine vector and parametric equations for the line through the point A(2, 5) with...

1. a.) determine vector and parametric equations for the line through the point A(2, 5) with direction vector = (1, −3). b.)Determine a vector equation for the line through the points (-1, 4) and (2, -1). c.) Determine parametric equations for the line through (-2, 3) and parallel to the line with vector equation = (−2, 1) + t(6, 4). d .) A line passes through the point (-4, 1) and is perpendicular to the line with parametric equations...

1.) Write a slope-intercept equation for a line passing through the point (5,−3) that is parallel...

1.) Write a slope-intercept equation for a line passing through the point (5,−3) that is parallel to the line 5x+7y=8. Then write a second equation for a line passing through the point (5,−3) that is perpendicular to the line 5x+7y=8. 2.) Write a slope-intercept equation for a line passing through the point (4,−3) that is parallel to the line 4x+5y=7. Then write a second equation for a line passing through the point (4,−3) that is perpendicular to the line 4x+5y=7....

Find point PP that belongs to the line and direction vector vv of the line. Express...

Find point PP that belongs to the line and direction vector vv of the line. Express vv in component form. Find the distance from the origin to line L. 251. x=1+t,y=3+t,z=5+4t,x=1+t,y=3+t,z=5+4t, t∈R answers are a- P=(1,3,5) V=<1,1,4> b. Square root of 3 I want all work shown please. I do not understand how to get root 3

The equation of the line that goes through the point (3,2) ( 3 , 2 )...

The equation of the line that goes through the point (3,2) ( 3 , 2 ) and is parallel to the line going through the points (−2,3) ( − 2 , 3 ) and (5,6) ( 5 , 6 ) can be written in the form ?=??+? where: m= b=

For the following exercises, write the vector shown in component form. Given initial point P1 = (2, 1) and terminal point P2 = (−1, 2), write the vector v in terms of ...

For the following exercises, write the vector shown in component form.Given initial point P1 = (2, 1) and terminal point P2 = (−1, 2), write the vector v in terms of i and j, then draw the vector on the graph.

Subjects