# p3 vectorsWatch

This discussion is closed.
#1
when you are given 3 points say A(x1,y1,z1) B(x2,y2,z2) and C(x3,y3,z3)
what is the formula to find the area of the triangle it makes

is it 1/2 x |AB| x |BC| ?
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#2
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13 years ago
#3
[1/2][(B-A)cross(C-A)]
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13 years ago
#4
(Original post by Freeway)
when you are given 3 points say A(x1,y1,z1) B(x2,y2,z2) and C(x3,y3,z3)
what is the formula to find the area of the triangle it makes

is it 1/2 x |AB| x |BC| ?
The formula you stated will only work if AB is at right angles to BC.
For a general triangle, you need to use:
Area=0.5absinc together with the scalar product.
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#5
so how would i find the area of PQR, if P is (3i+7j+3k) R is (4i+6j+8k) and Q is (2i+5j+4k)
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13 years ago
#6
(Original post by Freeway)
so how would i find the area of PQR, if P is (3i+7j+3k) R is (4i+6j+8k) and Q is (2i+5j+4k)
It might help you to draw out a sketch though you can do it without too.
The area of a triangle with sides a,b,c is 0.5absinc.
Note that sinc is the angle opposite side c, so the area is 0.5(Length of line a)(Length of line b)(sine of angle between lines a and b).
So, for this situation, you could say:
Area = 0.5[PR][PQ]sin(QPR).
And cos(QPR)=PQ.PR/[PQ][PR]
Where square brackets is supposed to mean modulus.
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