Posted by **Victor** on Tuesday, September 28, 2010 at 11:48pm.

Given vectors A = -4.8i + 6.8j and B = 9.6i + 6.7j, determine the vector C that lies in the xy plane perpendicular to B and whose dot product with A is 20.0.

- Vectors -
**Reiny**, Wednesday, September 29, 2010 at 12:18am
let the vector C = [a,b]

then using the dot product condition:

-4.8a + 6.8b = 20

or

12a - 17b = -50

slope of vector B is 6.7/9.6 or 67/96

slope of vector C is b/a

since the are perpendicualr

b/a = - 96/67

b = -96a/67

subbing back into first equation,

12a - 17(-96a/67) = -50

solving this I got

a = -1675/1218

and then back into the first ...

b = 400/203

so vector C = [-1675/1218, 400/203]

I will leave it up to you to check it out, it does work.

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