Vectors
– Addition, Multiplicaton, Direction Cosines
Vector Addition U
= (u1,u2,u3)
, V = (v1, v2, v3) 1-2-3 rectangular Cartesian coordinates Let u1 be the
component of U along the 1 axis; v1
be the component of V along the 1 axis u2 be the
component of U along the 2 axis; v2
be the component of V along the 2 axis u3 be the
component of U along the 3 axis; v3
be the component of V along the 3 axis Then by vector addition
(you add the components): U + V
= (u1 + v1
, u2 + v2 , u3
+ v3 ) |
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Magnitude of a vector U
= (u1,u2,u3) U =
√(u12 + u22 + u32 ) (square root of the sum of its
squares) |
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Unit Vector, eU, is the vector divided by its magnitude. eU =
U / | U | = U
/ U |
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Definition of the Base Unit Vectors - i, j,
k (along axes 1, 2, 3) i =
(1, 0, 0) j = (0, 1, 0) ,
k
= (0, 0, 1) |
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Copyright © 2017 Richard C. Coddington
All rights reserved.