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1)

For what values of a are the vectors i+3j-k and i+aj+k

i) inclined at 30 degree angle

cos@ = n1.n2 / |n1||n2|

cos^2(30) * 11(2+a^2) = ((3a)^2)

a=sqrt22

ii) perpendicular

(1,3,-1).(1,a,1)=0

1+3a-1=0

a=0

2)

Show that the lines

r=s(i+2j+3k)

r=(3i+5j+4k)+t(2i+3j+k)

intersect

I believe I should try and prove that they are not parallel. If their dot product is zero, then it means the lines are parallel. So if the answer is not zero, then I proved that the lines do intersect.

Do I just take the cross product of (1,2,3) and (2,3,1)? I want to know if I'm using the correct vectors to do the dot product.