{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mthsc206-fall-2010-notes-13.5

# mthsc206-fall-2010-notes-13.5 - 13.5 Equations of Lines and...

This preview shows pages 1–2. Sign up to view the full content.

13.5 Equations of Lines and Planes Lines in 3-space Question: What determines a line in 2-space? 3-space? Definition 13.5.1 The line through the point P 0 ( x 0 , y 0 , z 0 ) parallel to the vector v = < v 1 , v 2 , v 3 > is given by Example 13.5.1 Find parametric equations for the line through the points P (2 , 4 , - 1) and Q (5 , 0 , 7) . Find parametric equations for the line segment beginning at P and ending at Q . Problem 13.5.1 Given parametric equations for the points on a curve, how do you eliminate the param- eter? For example: if x = sin t, y = cos t, eliminate the parameter to find a cartesian equation of the curve. Definition 13.5.2 The symmetric equations for the line with given parametric equations x = x 0 + v 1 t, y = y 0 + v 2 t, z = z 0 + v 3 t are x - x 0 v 1 = y - y 0 v 2 = z - z 0 v 3 . Problem 13.5.2 How do you determine whether two lines are parallel? Definition 13.5.3 To lines are skew if they are not parallel and do not intersect. Problem 13.5.3 Let L 1 be the line with parametric equations L 1 : x = 1 + 2 t, y = 1 - 4 t, z = 5 - t, and let L 2 be the line with parametric equations L 2 : x = 4 - s, y = - 1 + 6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

mthsc206-fall-2010-notes-13.5 - 13.5 Equations of Lines and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online