# 3.3 - SECTION 3.3 SCALAR MULTIPLICATION 3 6 2 =-1-2 Let u...

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SECTION 3.3 SCALAR MULTIPLICATION: 3 2 1    6 2 = Let u be a vector; let c be a scalar; and set v = cu. (1) If c > 0, then v is in the same direction as u. (2) If c < 0, then v is in the opposite direction from u.

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The length or magnitude of a vector 1 2 u u u  =   is 22 12 uu u =+ Example: If uA B = !!!" where A=(3, 4) & B = (5, -1), find u 53 2 14 5 u == −− () ( ) 25 u 42 5 2 9 = (3) vc u = u 2u (-1/2)u
The vectors u and v are parallel provided there is a nonzero scalar c such that v = cu. Given that u & v are parallel, find a if 4 a v  =   and 3 2 u = So we know that v = cu 3 42 a c = 3 ac c = 4 = -2c means c = -2 So a = -6

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DEFN: A vector u is a unit vector provided 1 u = Example: 1 2 3 2 u = is a unit vector because 2 2 13 22 u  =+   11 44 = = Let v be a nonzero vector. Then 1 uv v = is a unit vector in the same direction as u.

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## This note was uploaded on 10/16/2009 for the course MATH 1114 at Virginia Tech.

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3.3 - SECTION 3.3 SCALAR MULTIPLICATION 3 6 2 =-1-2 Let u...

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