anonymous
  • anonymous
Find the distance of (1,0,0) from the line r=t(12i -3j -4k)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I shall take a numerical example because then I can explain both the principles and how the working out goes. Suppose the position vector of P from the origin O is OP = p = (2, -1, 2). Suppose that the vector equation of line L is r = (-1, 0, 7) + t (4, 1, -2). The shortest distance of P from L is given by the length of the perpendicular from P to L. Suppose this perpendicular meets L at H. Then we want to find the length of PH. There are two ways we can set about this. Method (1) Using the dot product Since H lies on L we can say that OH = h = (-1, 0, 7) + t (4, 1, -2) = (-1 + 4t, t, 7-2t) for some value of t which we need to find. Also, vector PH = -p + h = - (2, -1, 2) + (-1 + 4t, t, 7 - 2t) = (-3 + 4t, 1 + t, 5 - 2t). But PH is perpendicular to the direction vector (4, 1, -2) of line L. So the dot product of vector PH and (4, 1, -2) is zero. So (-3 + 4t, 1 + t, 5 - 2t).(4, 1, -2) = -12 + 16t + 1 + t - 10 + 4t = - 21 + 21t = 0 so t = 1. Therefore OH = h = (3, 1, 5) and vector PH = -p + h = (1, 2, 3). Its length |OH| is given by the square root of (1 + 4 + 9) = 3.74 to 2 sf. Method (2) Using the equation of a plane. Just as we found in method (1), we have h = (-1 + 4t, t, 7-2t). Now PH lies in a plane which is perpendicular to line L. So the direction vector (4, 1, -2) of L is perpendicular to this plane. Therefore it is a normal vector to the plane. Also, P lies in the plane. Using the equation of a plane of r.n = p.n, with r = (x, y, z), we get (x, y, z).(4, 1, -2) = (2, -1, 2).(4, 1, -2) so 4x + y - 2z = 3. But H also lies in this plane so we can say 4 (-1 + 4t) + t - 2 (7 - 2t) = 3 so 21t = 21 so t = 1 as before. hope this helps u!!
anonymous
  • anonymous
This doesn't help me much...
anonymous
  • anonymous
how

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
I don't know how to use this...
anonymous
  • anonymous
the answer is\[ \sqrt {69} \over 13 \]but I got 1/13
anonymous
  • anonymous
??
experimentX
  • experimentX
tan(alpha) = sqrt(1-cos2(alpha))/cos(alpha) = 5/13/12/13 = 5/12 5/12 = d/1 => d = 5/12 ???
anonymous
  • anonymous
that's not the answer...?

Looking for something else?

Not the answer you are looking for? Search for more explanations.