perpendicular vector

[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]

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?

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

[enpassant]

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

[Mao]

there's an infinite numbers of unit vectors perpendicular to this one (imagine it as an axis)

but to find "a" unit vector:

let a be a vector perpendicular to





one such set can be:



then