- #1
t_n_p
- 595
- 0
Homework Statement
What is the area of a triangle formed by the vectors 2i-j+3k and i+2j+2k.
The Attempt at a Solution
I didn't know it was possible to find the area with only 2 vectors!
Can somebody please show me how?
In summary, The conversation discusses finding the area of a triangle formed by two vectors in three dimensions. The original poster is unsure if it is possible and asks for help. Another user suggests using vector products and the original poster figures it out. It is mentioned that this is a standard problem in linear algebra, but not found in the original poster's textbook.
What is the area of a triangle formed by the vectors 2i-j+3k and i+2j+2k.
I didn't know it was possible to find the area with only 2 vectors!
Can somebody please show me how?
- #2
Alabran
- 27
- 0
I imagine the third side of said triangle is the length between both of the vectors.
That said, this seems to be a tricky problem because of the three dimensions involved, I'm thinking about it now.
That said, this seems to be a tricky problem because of the three dimensions involved, I'm thinking about it now.
- #3
t_n_p
- 595
- 0
I found this on the net...
Helpful?
Helpful?
- #4
t_n_p
- 595
- 0
Yeah i figured it out using vector products!
- #5
malawi_glenn
Science Advisor
Homework Helper
Gold Member
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t_n_p said:
Did you check your textbook in linear algebra? This is standard problems.
- #6
t_n_p
- 595
- 0
malawi_glenn said:
Wasn't in my textbook..
What is the formula for finding the area of a triangle formed by vectors?
The formula for finding the area of a triangle formed by vectors is A = 1/2 |a x b|, where a and b are the two vectors that form two sides of the triangle. |a x b| represents the magnitude of the cross product of the two vectors.
How do I find the vectors needed to calculate the area of a triangle?
To find the vectors needed, you will need to know the coordinates of the three vertices of the triangle. Then, you can use the coordinates to create two vectors, one from the first vertex to the second vertex and another from the first vertex to the third vertex.
Can the area of a triangle formed by vectors be negative?
No, the area of a triangle formed by vectors cannot be negative. The magnitude of the cross product in the formula always results in a positive value, and when multiplied by 1/2, it will always result in a positive area.
Is it necessary to use vectors to calculate the area of a triangle?
Yes, it is necessary to use vectors to calculate the area of a triangle. The cross product of two vectors is used to determine the area of a parallelogram, and since a triangle is half of a parallelogram, the formula for the area of a triangle involves dividing the magnitude of the cross product by 2.
Can the area of a triangle formed by vectors be greater than the sum of its side lengths?
No, the area of a triangle formed by vectors cannot be greater than the sum of its side lengths. This is because the formula for the area of a triangle formed by vectors involves taking the magnitude of the cross product, which is always less than or equal to the product of the magnitudes of the two vectors.
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