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# Vectors and Work

1 Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b

2 Given a=<4,5,-3> and b =<4,-2,2> determine whether a and b are parrallel, perpendicular, or neither.

3 Given F = 4i -2k;..... P(0,1,0) and Q(4,0,1) find the work W done by the force (F)moving a particle in a straight line from P to Q.

4 Given a =<1,2,3> and b=<4,5,6> find two different unit vectors, u an v, both of which are perpendicular to a and b.

#### Solution Preview

1 Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b

Multiply a with 7 and b with 9. We get
7a = 63i - 35j and 9b = 63i-36j.
Now subtract, we get
7a-9b=j.

Now multiply a with 4 and b with 5. We get
4a=36i-20j and 5b=35i-20j
Now subtract, we get
4a-5b=i
Hence i=4a-5b and j=7a-9b.

2 Given a=<4,5,-3> and b =<4,-2,2>determine whether a and b are parrallel, perpendicular, or ...

#### Solution Summary

Vectors and work are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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