- #1
_N3WTON_
- 351
- 3
Homework Statement
For the following vectors 'u' and 'v', express 'u' as the sum u = p + n where 'p' is parallel to 'v' and 'n' is orthogonal to 'v'
u = {-1, 2, 3}
v = {2, 1, 1}
Homework Equations
Dot product
Cross product
The Attempt at a Solution
First, I should say that I do not know how to use latex for determinants, so if somebody can help me out there I could make this problem a bit easier to read. Now, I am aware that two vectors are orthogonal if their dot product is 0 and parallel if their cross product is zero. I used this knowledge to attempt to solve the problem:
0 = p x v
0 = n 'dot' v
To attempt to figure out the value of p={a, b, c} I performed the cross product and obtained:
[itex] i (c-b) - j (2c-a) + k (2b-a) = 0 [/itex]
[itex] c = b [/itex]
[itex] 2c = a [/itex]
[itex] 2b = a [/itex]
Next, to attempt to figure out the value of n={x, y, z} I performed a the dot product and obtained:
[itex] (2, 1, 1) dot (x, y, z) [/itex]
[itex] 2x + y + z = 0 [/itex]
At this point I am not sure what to do, if somebody could give me some advice I'd greatly appreciate it.