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December 21, 2014

December 21, 2014

Posted by **Anonymous** on Monday, March 17, 2008 at 9:52pm.

QUESTION:

Show that the lines:

r = (4,7,-1) + t(4,8,-4)

r = (1,5,4) + u(-1,2,3)

intersect at right angles and find POI.

============================

ATTEMPT:

v = (4,8,-4) x (-1,2,3)

v = (32,-8,16)

v = (4,-1,2)

Finding POI:

l_1:

x = 4 + 4t

y = 7 + 8t

z = -1 - 4t

l_2:

x = 1 - u

y = 5 + 2u

z = 4 + 3u

(1) 3 = -u - 4t

(2) 2 = 2u - 8t

(3) -5 = 3u + 4t

Find "t", sub (1) into (2):

t = 1/2

Find "s", sub "t" into (2):

u = 3

Verify (3):

LS:

= -5

RS:

= 3(3) + 4(1/2)

= 11

Therefore, LS does not equal RS, so skew

========================

TEXTBOOK ANSWER:

(2,3,1)

- Math: Equations of Lines -
**Reiny**, Monday, March 17, 2008 at 10:22pmfirst of all if two lines are perpendicular, then the "dot product" of their direction vectors must equal zero, so

(4,8,-4)∙(-1,2,3) = -4+16-12 = 0

so they are perpendicular.

btw, I had t = +1/2 and u = -1 but it did not check out in the third.

so they are skew but at right angles.

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