Hello!

We got an assignment in a Calculus class that appears to me to be very linear algebra-ish... I can do some of it by intution but I have two questions,

(Q1)

To show the

line (L1):

containing the points (3,10,5) and (8,15,15)

and the

line (L2):

x= 3 + 2t

y= 4 - t

z= -1 + t

intersect,

and finding the angle between them.

I don't have a strong linear background. I believe their intersection of L1 and L2 is at (1,6,-3) (and therefore they intersect).

I am not sure how to begin on finding the angle between them. Does the cross product have an application here? Not sure exactly what the cross product represents, so I am not sure how to use it, but I know it involved the sine of the angle between the two lines...

(Q4)

Let L be the intersection of two planes,

x + y + z = 4

and

3x - y = 5

(a) find parametric equations for L

(b) Find an equation of the plane through the points (1,0,-1) and (2,1,0) that is also parrallel to L.

For part (a), I am assuming L represents a line, however I am not sure how to get L in standard form, let alone parametrically.

also in part (b) I think I know that the dot product of the plane and the line will be 0, if the plane is parrallel to the line?

Sorry if these questions are in the wrong area of the forum, they seem like very linear-algebra-related questions in a calculus course.

Thanks!