I DON'T KNOW HOW TO RETRIEVE THE TEXTBOOK ANSWER!

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.

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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

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TEXTBOOK ANSWER:

(2,3,1)