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
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?
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?
You just learn the rule for projections.
$\displaystyle \text{proj}_v u = \frac{{u \cdot v}}
{{\left\| v \right\|^2 }}v = \frac{8}
{{14}}\left\langle {3,2, - 1} \right\rangle $
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