Posted by **Raven** on Sunday, May 30, 2010 at 3:34pm.

The two lines with the equation r=(1,2,-44)+ t(k+1, 3k+1,k-3) and x=2-3s, y=1-10s, z=3-5s, are given.

a) determine the vaulue for K when the lines are paralel

b) determine the value of K when the lines are perpendictular

- Vector -
**Damon**, Sunday, May 30, 2010 at 7:50pm
Vector 1 = (K+1) i +(3K+1)j + (K-3) k

Vector 2 = -3 i -10 j -5 k

If those are parallel the cross product is zero

i j k

K+1 3K+1 K-3

-3 -10 -5

i term -5(3K+1) + 10(K-3) = 0

K = -7

same for j and k directions, K = -7

If they are perpendicular the dot product is 0

(K+1)(-3) +(3K+1)(-10) + (K-3)(-5) = 0

solve for K

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