in this problem. on the Example 2 page where it states uOA= -2/3 i+ 2/3j+1/3k wh

Question

in this problem. on the Example 2 page
where it states uOA= -2/3 i+ 2/3j+1/3k
where did the 3 come from

Given: The force acting on the pole at point A. The components of the force acting parallel and perpendicular to the axis of the pole. F 600 I1b Find: Plan: 1. Find F, ror and uo 2. Determine the parallel component of F using F 3. The perpendicular component of F is F( 0A F 0A Copyright ©2016 by Pearson Education, Inc. p E A R SON ALWAYS LEARNING R.C. Hibbeler Statics, Fourteenth Edition All rights reserved

Explanation / Answer

Here uOA is unit vector.

In general unit vector = vector / magnitude of vector

Any vector can become a unit vector by dividing it by vectors magnitude.

in this case, vector is rOA = -4 i +4j + 2k

magnitude of rOA is | rOA | = { (-4)2 + (4)2 + (2)2 } 1/2 = 6

unit vector uOA = rOA / | rOA |

uOA = (-4 i +4j + 2k ) / 6

uOA = (-4 /6 )i + (4/6 ) j + (2/6 ) k

uOA = ( -2/3 ) i + ( 2/3 ) j + (1/3 ) k

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