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THe question i encountered is this:
r = 5i + 3j – 2k + λ(i – 2j + 2k)
r = 2i – 11j + 14k +μ(-3i – 4j + 5k)
Given that the two lines intersect, find the acute angle between the two lines
Thank you in advance!

2006-06-13 17:32:41 · 3 answers · asked by freezerfairy 1 in Science & Mathematics Mathematics

3 answers

since you claim both lines intersect,
5+λ=2+μ (in direction i, both lines reach the same point)
3-2λ=-11-4μ (in direction j, both lines reach the same point)
solving the above,
μ=-10 λ=-13
We can substitute λ and μ in the k direction, and verify whether both lines really intersect:
-2+2(-13)=-28
14+5(-10)=-36

Both lines do not intersect

2006-06-13 18:18:49 · answer #1 · answered by peaceharris 2 · 1 0

u have got da variable mu and lamda parts right. da vectors after dat are da dirctions of da two vectors. for example ur first eqn points in da direction of a line from origin (1,-2,2) n it goes through (5,3,-2). ok wit dat taken care of to find da angle u have to get da dot product of da two vectors dat shows da directions. yep dats da two vectors after mu and lamda. cross product is found by multiplying corresponding coefficents of two vectors by each other. so coefficent of i in first one is multiplied by coefficent of i in da second one to give -3. finally all da three values are added up. do it and see. u should get 13. hope it help. if u need any help drop in a 360 message or a mail.

2006-06-13 17:45:58 · answer #2 · answered by Raven 2 · 1 0

the the dot product of the two vectors duh!

2016-03-27 03:18:45 · answer #3 · answered by Anonymous · 0 0

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