The rectangular prism is measured 1x2x3 as shown, find the the projection of vector u onto vector v.

i'm having trouble finding the points of u and v

my guess:

u(1,0,3)

v(1,2,3)

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- Aug 27th 2009, 05:43 PMskeske1234Projection of Vectors
The rectangular prism is measured 1x2x3 as shown, find the the projection of vector u onto vector v.

i'm having trouble finding the points of u and v

my guess:

u(1,0,3)

v(1,2,3) - Aug 27th 2009, 05:55 PMCalculus26
The formula for the projection of u on v is

proj**u**on**v**= (**u*****v**/||**v**||^2)**v**

what you are using for u and v is incorrect

u = (3,0,1) v = (3,2,-1) - Aug 28th 2009, 02:58 AMenjam
The projection of u along v is simply:

u . v/|v|

So you have:

(3i + 0j + k) . (3i + 2j - k) / (3^2 + 2^2 + (-1)^2)^0.5

= (3x3) + (0x2) + (1x-1) / (14)^0.5

= 8 / sqrt 14 - Aug 28th 2009, 05:26 AMskeske1234
How did you get the x value to be 3? isn't the x value the width/depth of the rectangular prism, thus 1? and the height 3 = z value and the length 2=y value?

- Aug 28th 2009, 06:50 AMPlato
- Aug 28th 2009, 01:22 PMCalculus26Quote:

The projection of u along v is simply:

u . v/|v|

So you have:

(3i + 0j + k) . (3i + 2j - k) / (3^2 + 2^2 + (-1)^2)^0.5

= (3x3) + (0x2) + (1x-1) / (14)^0.5

= 8 / sqrt 14

The projection is a vector --what you have here is the magnitude of the projection - Aug 28th 2009, 05:19 PMskeske1234
Plato, I mean how did you get the point (3,2,-1)? like the vector points of u and v, in order to plug in formula

- Aug 28th 2009, 05:28 PMCalculus26
At firs tglance it appears as though u goes from(0,0,1) to (3,0,1)

so u should b3 3i not 3i + k as I suggested

and v goes from (0,0,1) to (3,2,0) v = 3 i + 2j -k