Math Is Fun Forum

rzaidan

Member

Registered: 2009-08-13

Posts: 59

vectors

find a unit vector parallel to a plane determined by the two vectors     3i -2j +k   ,     i + j - 2 k   and perpendicular to the vector   2i+2j-k
plz  help as soon as possible

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: vectors

hi rzaidan,

This question had me puzzled for a while because I was mis-interpreting it.  All because of an ambiguous AND.

I thought it meant:

Find a unit vector parallel to a plane. 

The plane has these properties :

It is (i) determined by the two vectors  3i -2j +k   ,   i + j - 2 k   AND  (ii) it is perpendicular to the vector   2i+2j-k

This is impossible.

I have thought about it, and now I think the question means this:

Find a unit vector parallel to a plane AND  perpendicular to the vector   2i+2j-k. 

The plane is  determined by the two vectors     3i -2j +k   ,     i + j - 2 k   

So how to do this.

Find any vector that fits the requirements and, at the end,  make it a unit vector.

If the vector lies in that plane it can be expressed as a linear combination of the two vectors

V = L( 3i -2j +k ) + M( i + j - 2 k)  where L and M are two scalars.

So form the scalar product (dot product) of V with   2i+2j-k and set this equal to zero.

This will fix L in terms of M.  It won't fix M as well but that is OK as there are many parallel vectors with these properties.  Just choose M to be something ... might as well choose M = 1 to keep things easy.  Calculate L and hence V.

Now use Pythagoras to find |V| and divide each component by this number.  V / |V| will be the required unit vector.

Hope that helps. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: vectors

thnx dear