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Let u=(4,0,1), v=(5,1,0), and w=(3,1,2).
Find the area of the triangle determined by u and v.
 2 years ago
 2 years ago
Let u=(4,0,1), v=(5,1,0), and w=(3,1,2). Find the area of the triangle determined by u and v.
 2 years ago
 2 years ago

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slaaibakBest ResponseYou've already chosen the best response.2
I think the area for the parallelogram would be the length of the cross product. u x v
 2 years ago

slaaibakBest ResponseYou've already chosen the best response.2
Therefore, the area of the triangle would be the half of }u x v
 2 years ago

shelovespianoBest ResponseYou've already chosen the best response.0
Could you write it out? I'm a little confused, I guess.
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
what have you some up with in the cross product so far?
 2 years ago

shelovespianoBest ResponseYou've already chosen the best response.0
I have (20, 0, 0) but I feel like I've done something wrong... I'm not very good with vectors.
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
\[\begin{vmatrix}X&Y&Z\\U_x&U_y&U_z\\V_x&V_y&V_z\end{vmatrix}\to X\begin{vmatrix}\\U_y&U_z\\V_y&V_z\end{vmatrix} Y\begin{vmatrix}\\U_x&U_z\\V_x&V_z\end{vmatrix} +Z\begin{vmatrix}\\U_x&U_y\\V_x&V_y\end{vmatrix}\]
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
thats the "formal" confusion for it: me, i just do this x 4 5 x = 1 y 0 1 y = 5 z 1 0 z = 4
 2 years ago

shelovespianoBest ResponseYou've already chosen the best response.0
How does what you just did work?
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
so, the length of the vector <1,5,4> its the same process as the fancy typing; but in a vertical format that I can keep track of better
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
turn the matrix on its side pretty much and expand down the first column; taking the determinant of each sub matrix along the way
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
<1,5,4> ^2 = 1 + 25 + 16 = sqrt(42) sqrt(42)/2 = area triangle
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
there are other ways to do it if you cant cross that well :)
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
but the cross bypasses any trig you might not know
 2 years ago

shelovespianoBest ResponseYou've already chosen the best response.0
Ok. I think this works pretty well for me:P
 2 years ago
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