- #1
geft
- 148
- 0
Homework Statement
There are two questions,
1) straight line through (2, 0, 4) and (-3, 0, 9)
2) straight line y = 2x + 3, z = 7x
Homework Equations
r(t) = a + tb = [a1 + tb1, a2 + tb2, a3 + tb3]
The book also explains how to calculate the line if b is a unit vector, but I don't understand what it is trying to say (directional cosines?). For instance, the straight line in the xy-plane through A: (3,2) having slope 1 is:
r(t) = [3, 2, 0] + t[1, 1, 0] = [3 + t, 2 + t, 0]
I don't understand how exactly does having slope of 1 translate to [1, 1, 0].
The Attempt at a Solution
For (1), I get the vector (-5, 0, 5) by subtracting the vertices, but I have no idea how to get the second vector to plug into the equation above.
For (2), (x, y, z) = (x, 2x + 3, 7x). Suppose x = 1, then (x, y, z) = (1, 5, 7). Suppose x = 0, then (x, y, z) = (0, 3, 0). Subtracting those to get a vector, I get (1, 2, 7). Like in (1), I don't know how to get a second vector.