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# P3 Vectors.... watch

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1. FInd a vector which is perpendicular to both a and b where:

e) a = 2i - 3j - 4k, b = 4i -3j + k

CHeers.
2. 5i + 6j - 2k.
3. (Original post by jonnymcc2003)
FInd a vector which is perpendicular to both a and b where:

e) a = 2i - 3j - 4k, b = 4i -3j + k

CHeers.
It looks impossible - two equations and three unknowns

MB
4. No the guy above got it right.

The method would be nice however...
5. Sorry, I used the cross product and did the working in my head. However, if you would like a passable P3-style solution:

Let the vector you want be xi + yj + zk.

If you dot this vector with your two given vectors, you get 0

=> 2x - 3y - 4z = 0
and 4x - 3y + z = 0

Like musicboy said, there are two equations and three unknowns, so you cannot obtain a unique solution of x, y and z. However, all the possible values of x, y and z will be scalar multiples of each other, so it doesn't matter.

Equate your two equations to give:

-2x = 5z

Therefore 1.2x = y

Stick in any value of x (say 1)

Thus your vector is 1i + 1.2j - 0.4k

or multiply it thrhough by 5 to get integer coefficients of i, j and k.

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Updated: June 7, 2004
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