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perpendicular vector

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enpassant:
find a unit vector perpendicular to both 2i - j and i + 3j.

Collin Li:
There are none in two dimensional space. If we assign them 0k, we can find some in three dimensional space:

Let some vector ai + bj + ck be perpendicular to 2i - j and i + 3j.

and

Solving these sets of simultaneous equations yields

This means the vector perpendicular to both those vectors must have while is a 'free' variable (can choose anything).

However, for a unit vector, .

Therefore, are unit vectors perpendicular to both 2i - j and i + 3j.

evaporade:
Obviously +/-k is a unit vector perpendicular to 2i - j and i + 3j because both are in the x-y plane (i-j plane). So is it necessary to do the working as suggested?

Collin Li:

--- Quote from: evaporade on April 03, 2008, 07:16:12 am ---Obviously +/-k is a unit vector perpendicular to 2i - j and i + 3j because both are in the x-y plane (i-j plane). So is it necessary to do the working as suggested?

--- End quote ---

Perhaps in Specialist Maths, yes, since geometry is not taught properly.

enpassant:
find a unit vector perpendicular to i - 2j + 3k

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