3.5 - 3.5 Vectors in 3 Space Let A= (a1, a2, a3) and B =...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
3.5 Vectors in 3 Space Let A= (a 1 , a 2 , a 3 ) and B = (b 1 , b 2 , b 3 ) be points in 3-space. (1) The midpoint of the line segment AB is 33 11 2 2 ,, 222 ab a b + ++    (2) The distance between A and B is d(A , B)= () ( ) ( ) 2 2 3 3 ba b a −+ + The components of AB are: 22 xcomponent b a ycomponent b a zcomponent b a   =−  ||u|| = d(A, B)
Background image of page 1

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

View Full DocumentRight Arrow Icon
If 1 2 3 u uu u   =  then 222 123 u u =+ + . Basic Unit Vectors 1 0 0 i = 0 1 0 j = 0 0 1 k = If a ub c = then 10 0 01 0 00 1 u abc =++ ai bj ck
Background image of page 2
Example: 34 2 . . u i j and v j k Find uv =+ = + + 303 42 6 01 1   +=  or you can do it by adding like terms. Example: Find a vector 6 units long in the same direction as V=3i - 4j + k. 22 2 66 26 3( 4 )1 vv = +− + Example: Let vA B = !!!" where A=(3, 0, -1) and B=(4, 3, 5). If u is in the same direction as v and 1 2 = f find Q such that
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

3.5 - 3.5 Vectors in 3 Space Let A= (a1, a2, a3) and B =...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online