Question

I need help with Linear algebra

Answer 1

1)find parameterization of P and Q
2) find \(\vec {PQ}\)
3) let \(\vec{PQ} . d_1=0\) (dot product)
4)\(let\vec {PQ} .d_2 =0\)
5) solve for s, t.

Answer 2

i've tried this many times...but for some reason I make a mistake somewhere and I get the whole thing wrong...This question is getting annoying for me

Answer 3

6) take length of PQ

Answer 4

ok, what is P ?

Answer 5

wait by PQ do u mean P1P2?

Answer 6

yes

Answer 7

p1p2= [-5 11 -12]^t

Answer 8

not that
L1 has d1 = <-1,0,1> , P1 (-8,-5,7), hence parameterization P1 is < -8 -t, -5, 7 +t>
do the same for P2 , we have P2 =<-13 , 6-2s , -5-s >

Answer 9

then vector P1P2 is < -13 +8+t, 6-2s +5, -5-s -7-t>

Answer 10

ya

Answer 11

Now take dot product with d1
(-13 +8+t)(-1) + (-5-s-7-t) (1) =0
then -5-s-2t =0

Answer 12

take dot product with d2
(6-2s+5)(-2)+(-12-s-t)(-1) =0
-10+5s+t=0

Answer 13

solve for s, t, your turn

Answer 14

wait for the first system of equation should it be -7-s-2t=0

Answer 15

oh yeah, you are right, sorry my bad

Answer 16

no problem

Answer 17

ok, then s = 3, t =-5, right?

Answer 18

Plug back to get vector P1P2

Answer 19

yup

Answer 20

i got [-10 5 -10]^T

Answer 21

I plugged the values into this P1P2 is < -13 +8+t, 6-2s +5, -5-s -7-t>

Answer 22

gosh!! I keep calculating -13 +8 =-7 how dummy I am!! Sorry friend, you are right

Answer 23

No worries im just glad ur helping me lol

Answer 24

ok, now take the length of it

Answer 25

I got 15