# Vectors and the Geometry of Space

Line 1 and line 2 are given by equation 1 and 2. Point A has coordinates (xo, yo, zo). Find the equation of line 3 which goes through A and crosses L1 and L2.

mathman
Line 1 and line 2 are given by equation 1 and 2. Point A has coordinates (xo, yo, zo). Find the equation of line 3 which goes through A and crosses L1 and L2.
You failed to include equations 1 and 2.

Equation 1 and 2 are not supposed to be given.

LCKurtz
Homework Helper
Gold Member
Line 1 and line 2 are given by equation 1 and 2. Point A has coordinates (xo, yo, zo). Find the equation of line 3 which goes through A and crosses L1 and L2.

Suppose line 1 is R1(t) = P + tD1
Line 2 is R2(s) = Q + sD2

where the P and Q are given points and the D's are given direction vectors.

Then a line from one to the other would be
R3(u) = R1(t) + u(R2(s)-R1(t))

Set that equal to your given point. You have three given coordinates of the point and three parameters s,t, and u to work with.

I don't understand why you put R1(t) as the r0 vector in the R3(u) vector equation instead of just inputting the given point A there.

LCKurtz