Question

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

Answer 1

Isn't it dot product which finds the area?

Answer 2

You can use the origin (0,0) as the common start point for those two vectors; that would make it easiest to draw.

Answer 3

No, 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 thisbut very low area (dottiness=cos(angle between vectors))

Answer 4

Cross product most likely, but forget about the result being a vector.

Answer 5

Oh, that's right, cross product because it is a*b*sin(Θ).

Answer 6

b*sin(Θ) is the height of the parallelogram. Duh, should have remembered the basic trig on that one.

Answer 7

Is there any way to solve for the area without trig?

Answer 8

Not really...

Answer 9

Well, doing the cross-product has the trig built-in, so you wouldn't actually be using a trig function explicitly.

Answer 10

I suppose you could try to use pythagoras

Answer 11

^ what do you mean? By stacking up right triangles and using subtraction?

Answer 12

find B perpendicular with A by finding the 'gradient' of A... you can do it, but it's really fiddly