Calculus

posted by .

Find the distance between the lines [x,y,z] = [-1,1,0] + s[3,4,-2] and [x,y,z] = [5,9,-4] + t[2,3,1]. Interpret the result.

  • Calculus -

    As I recall, if you have two lines

    L1: p1 + v1*t
    L2: p2 + v2*t

    the distance can be obtained by projecting the unit normal between the lines onto the line joining the two points:

    v1 × v2 / |v1 × v2| • (p1 - p2)

    For a brief example and discussion, see

    physicsforums . com / showthread.php?t=276253

  • Calculus -

    for this question, do i have to solve it? it just says interpret the results, does that mean only explain?

    im trying to solve it right now. i have:

    L1: [x,y,z]=[-1,1,0]+s[3,4,-2]
    L2: [x,y,z]=[5,9,-4]+t[2,3,1]

    First, cross product of the two directional vectors from both lines:

    [3,4,-2] x [2,3,1] =


    That's all I have so far :/
    I don't know what to do next because in the example shown on the forum, I don't know how they got the answer [from the forum: (-2,3,-2) x (-2,-3,-1) = (-9,-2, 12)] I know 3 x (-3) is -9 but I don't understand where the -2 and +12 came from since (-2)(-2) = +4 and (-2)(-1)= +2.

    Also on the forum there is:

    And its unit vector is:
    -9x-2y+12z
    -----------
    229^1/2

    I don't know how they got this answer either. They mentioned at the end of it they may not be right so I don't know ....

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus (for Business)

    Suppose a fish swimming a distance of L ft at a speed of v fit/sec relative to the water against a current flowing at the rate of u ft/sec (u<v) expends a total energy given by E(v)= (aLv^3)/(v-u) Where E is measured in foot-pounds …
  2. calculus

    The efficiency of an internal combustion engine is given by E= (1-v/V)^0.4 Where V and v are the respective maximum and minimum volumes of air in each cylinder. a) Show that ∂E/ ∂V > 0 and interpret your result b) Show …
  3. calculus

    The efficiency of an internal combustion engine is given by E= (1-v/V)^0.4 Where V and v are the respective maximum and minimum volumes of air in each cylinder. a) Show that ∂E/ ∂V > 0 and interpret your result b) Show …
  4. Calculus

    Find the shortest distance between the two skew lines L1 and L2 with equations r = [1,2,2] + s [4,3,2] and r = [1,0,-3] + t [4,-6,-1]
  5. Math (Algebra) (Distance Between 2 Lines)

    If real numbers a and b satisfy a^2 + b^2 = 64, what is the distance between the lines ax + by = 1 and ax + by = 417 ?
  6. Math (Algebra) (Distance Between 2 Lines)

    If real numbers a and b satisfy a^2 + b^2 = 64, what is the distance between the lines ax + by = 1 and ax + by = 417 ?
  7. Physics

    Two charges +q and −q are separated by a distance d=50 cm. The electric field lines for this system form the the well-known pattern showed in the figure below. Consider two lines L1 and L2 lying on the same plane and leaving …
  8. math

    Consider the following hypothesis statement using alpha = .05, and data from two independent samples: Ho: µ1 - µ2 = 0 Ha: µ1 - µ2 not equal to 0 X1 = 237, X2 = 218 ¬1 = 54, ¬2 = 63 n1 = 42, n2 = 35 a) Calculate the appropriate …
  9. Math.stat help :(

    Consider the following hypothesis statement using alpha = .05, and data from two independent samples: Ho: µ1 - µ2 = 0 Ha: µ1 - µ2 not equal to 0 X1 = 237, X2 = 218 ¬1 = 54, ¬2 = 63 n1 = 42, n2 = 35 a) Calculate the appropriate …
  10. distance

    find the distance between lines whose equations are: y=-1/4x+2 and y=-1/4x-9/4. d=ã(1-(-3)^2 +(1-2)^2

More Similar Questions