jerri-3-5

# jerri-3-5 - 3.5 Vectors in 3 Space Let A=(a1 a2 a3 and B...

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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)

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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
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

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jerri-3-5 - 3.5 Vectors in 3 Space Let A=(a1 a2 a3 and B...

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