Posted by Raven on .
The two lines with the equation r=(1,2,44)+ t(k+1, 3k+1,k3) and x=23s, y=110s, z=35s, 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,
Vector 1 = (K+1) i +(3K+1)j + (K3) 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 K3
3 10 5
i term 5(3K+1) + 10(K3) = 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) + (K3)(5) = 0
solve for K