If you take note of the definition of vector cross product for example on:
https://en.wikipedia.org/wiki/Cross_product
you will learn that the cross product of vectors a and b is a vector (for example c) that is perpendicular to both a and b, and its length is:
|c| = |a|.|b|.Sin(θ)
However, the above definition leads to a contradiction.
Let's say:
a is a vector with its length being 3 meters.
b is a vector with its length being 4 meters.
and a and b are perpendicular to each other
And c = a × b
I calculate the length of c in two different ways:
Method 1:
|a| = 3 m
|b| = 4 m
θ = 90
|c| = |a|.|b|.Sin(θ) = 3m × 4m × Sin(90) = 12m
Method 2:
|a| = 3 m = 300 cm
|b| = 4 m = 300 cm
θ = 90
|c| = |a|.|b|.Sin(θ) = 300m × 400m × Sin(90) = 120000 cm = 1200m
Why two diferent ways of calculation leads to two different results?
So, which one is correct?
And what is wrong with the above two methods of calculation?
Please advise.
Thanks.
https://en.wikipedia.org/wiki/Cross_product
you will learn that the cross product of vectors a and b is a vector (for example c) that is perpendicular to both a and b, and its length is:
Quote:
|c| = |a|.|b|.Sin(θ)
Let's say:
a is a vector with its length being 3 meters.
b is a vector with its length being 4 meters.
and a and b are perpendicular to each other
And c = a × b
I calculate the length of c in two different ways:
Method 1:
|a| = 3 m
|b| = 4 m
θ = 90
|c| = |a|.|b|.Sin(θ) = 3m × 4m × Sin(90) = 12m
Method 2:
|a| = 3 m = 300 cm
|b| = 4 m = 300 cm
θ = 90
|c| = |a|.|b|.Sin(θ) = 300m × 400m × Sin(90) = 120000 cm = 1200m
Why two diferent ways of calculation leads to two different results?
So, which one is correct?
And what is wrong with the above two methods of calculation?
Please advise.
Thanks.