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Copythat
 3 years ago
Draw a parallelogram whose adjacent sides are determined by the vectors [4,6] and [3,5]. Find the area of the parallelogram.
Copythat
 3 years ago
Draw a parallelogram whose adjacent sides are determined by the vectors [4,6] and [3,5]. Find the area of the parallelogram.

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CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1Isn't it dot product which finds the area?

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1You can use the origin (0,0) as the common start point for those two vectors; that would make it easiest to draw.

henpen
 3 years ago
Best ResponseYou've already chosen the best response.1No, I don't think it's dot product, as dot product is a measure of how much the vectors are in each other's direction, so it would have high dottiness if they were like thisdw:1350760137445:dwbut very low area (dottiness=cos(angle between vectors))

henpen
 3 years ago
Best ResponseYou've already chosen the best response.1Cross product most likely, but forget about the result being a vector.

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1Oh, that's right, cross product because it is a*b*sin(Θ).

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1b*sin(Θ) is the height of the parallelogram. Duh, should have remembered the basic trig on that one.

Copythat
 3 years ago
Best ResponseYou've already chosen the best response.0Is there any way to solve for the area without trig?

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1Well, doing the crossproduct has the trig builtin, so you wouldn't actually be using a trig function explicitly.

henpen
 3 years ago
Best ResponseYou've already chosen the best response.1I suppose you could try to use pythagoras

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1^ what do you mean? By stacking up right triangles and using subtraction?

henpen
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1350764732234:dw find B perpendicular with A by finding the 'gradient' of A... you can do it, but it's really fiddly

henpen
 3 years ago
Best ResponseYou've already chosen the best response.1No there must be an elegant way of finding B perp A

henpen
 3 years ago
Best ResponseYou've already chosen the best response.1as a function of Ax, Bx, Ay and By

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1I'd rather just do the crossproduct.

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.1\[\left[\begin{matrix}i & j & k \\ 4 & 6 & 0 \\ 3 & 5 & 0\end{matrix}\right] = 4\times5  6\times3=2\]
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