# How do I start this vector problem

• Sep 5th 2008, 03:54 PM
Allie
How do I start this vector problem
http://mathcs.chapman.edu/webwork2_f...38556e3171.png and http://mathcs.chapman.edu/webwork2_f...37768eabf1.png, find a unit vector with positive first coordinate orthogonal to both http://mathcs.chapman.edu/webwork2_f...6067c94d71.png and http://mathcs.chapman.edu/webwork2_f...1571a542a1.png.

I can do the calculation myself, i'm just not sure where to start
• Sep 5th 2008, 07:24 PM
mr fantastic
Quote:

Originally Posted by Allie
http://mathcs.chapman.edu/webwork2_f...38556e3171.png and http://mathcs.chapman.edu/webwork2_f...37768eabf1.png, find a unit vector with positive first coordinate orthogonal to both http://mathcs.chapman.edu/webwork2_f...6067c94d71.png and http://mathcs.chapman.edu/webwork2_f...1571a542a1.png.

I can do the calculation myself, i'm just not sure where to start

Start by taking the cross product of a and b.
• Sep 6th 2008, 11:12 AM
Allie
I did do that is there another step? I seem to be missing omething
for the dot product i get
(10i+j+20k)-(20i+j-10k) which would give me -10i+10k. I know the j coefficient is 0 but where did i go wrong with the others?
• Sep 6th 2008, 02:40 PM
mr fantastic
Quote:

Originally Posted by Allie
I did do that is there another step? I seem to be missing omething
for the dot product i get
(10i+j+20k)-(20i+j-10k) which would give me -10i+10k. I know the j coefficient is 0 but where did i go wrong with the others?

I said cross product, not dot product.

Are you aware there are two different way of multiplying two vectors? Have you been taught how to take the cross product of two vectors?
• Sep 6th 2008, 04:19 PM
Allie
yes im aware and i did the cross product i don't know why i said dot.
• Sep 6th 2008, 04:31 PM
mr fantastic
Quote:

Originally Posted by Allie
yes im aware and i did the cross product i don't know why i said dot.

So -10i+10k is perpendicular to a and b. Obviously any scalar multiple of -10i+10k is also perpendicular. So 10i - 10k is perpendicular (and satisfies the requirement of the i-component being positive).

Do you know how to get a unit vector in the direction of 10i - 10k ?
• Sep 6th 2008, 04:51 PM
Allie
yes you have to divide it through by the magnitude thank you
• Sep 6th 2008, 04:56 PM
mr fantastic
Quote:

Originally Posted by Allie
no

You know how to do a cross product but can't construct a unit vector!?

Divide 10i - 10k by its magnitude.