Finding the Point of Intersection and Acute Angle between Two Lines

[nk735]

Homework Statement

Prove that the lines r=(a,b,c)+t(d,e,f) and q=(h,i,j)+s(k,l,m) intersect, and find the coordinates of their point of intersection. Also, find the acute angle between their lines

Homework Equations

The Attempt at a Solution

I have no attempt because I'm stumpped...

 

[HallsofIvy]

Do you understand that "r= (a,b,c)+ t(d,e,f)" means that x= a+ td, y= b+ te, z= c+ tf for every point on that line and that "q= (h,i,j)+ s(k,l,m)" means that x= h+ sk, y= i+ sl, z= j+ sm for every point on THAT line. If the two lines intersect then, at the point of intersection they have the same x, y, z values: x= a+ td= h+ sk, y= b+ te= i+ sl, z= c+ tf= j+ sm. That gives you three equations to solve for t and s.

Of course, typically, you can use two of those equations to find t and s and the check in the third to see if they work. Typically, two lines in 3 dimensions do NOT intersect.

 

[nk735]

Ok, I've managed to get the point of intersection from that, thankyou. But what about the acute angle between them?