Calculating area of a parallelogram defined by 2 vectors

AI Thread Summary
The area of a parallelogram defined by vectors P=(4,-10,3) and Q=(2,1,0) is calculated using the magnitude of the cross product of the two vectors. The attempted calculation of the cross product resulted in a scalar value of 25, which is incorrect. The correct cross product should yield a vector, and the area is the magnitude of that vector. The notation | | indicates the magnitude of the vector resulting from the cross product. Understanding how to compute the cross product correctly is essential for finding the area.
WinstonB
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Homework Statement



"Find the area of a parallelogram defined by the two vectors P=(4,-10,3) and Q=(2,1,0)"

Homework Equations



The area of the parallelogram is equal to the magnitude of the cross product of the two vectors? i.e. Area = |PXQ|

The Attempt at a Solution



PXQ = (-10x0-3x1)-(4x0-3x2)-(4x1-(-10)x2)=-3-(-6)-(-16)=25

-> area of parallelogram = 25(?)
 
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WinstonB said:

Homework Statement



"Find the area of a parallelogram defined by the two vectors P=(4,-10,3) and Q=(2,1,0)"

Homework Equations



The area of the parallelogram is equal to the magnitude of the cross product of the two vectors? i.e. Area = |PXQ|

That is right.

WinstonB said:

The Attempt at a Solution



PXQ = (-10x0-3x1)-(4x0-3x2)-(4x1-(-10)x2)=-3-(-6)-(-16)=25

-> area of parallelogram = 25(?)

The cross product is a vector - you wrote a scalar. Check how to calculate a vector product.

ehild
 
so I should have = 3i - 6j + 24k?

I can't see how to get an area from the vectors.
 
The formula you wrote was "Area = |PXQ|". What does the | | mean?
 

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