Two problems:
The negative sign is important- it'll give you a different value for u, also.
To show two vectors are perpendicular, use the dot product, not the cross product.
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)