parallel vectors
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hi guys.. If two vector are parallel that means both the line are parallel aslo? i confuse..
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Originally posted by ZaiDancerz:
hi guys.. If two vector are parallel that means both the line are parallel aslo? i confuse..
Yes.
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ok.. normally question nid to use this to prove similar triangle and find area?
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Originally posted by ZaiDancerz:
ok.. normally question nid to use this to prove similar triangle and find area?
Sorry but I have no idea but you mean by normally ( as in under what context ). : X
But vectors can indeed be used to prove similar triangles and find areas.
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can u giv me one example? can steps to do it? thanks alot ya...
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Originally posted by ZaiDancerz:
can u giv me one example? can steps to do it? thanks alot ya...
why not you give an example and we solve it instead =)
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Originally posted by ZaiDancerz:
can u giv me one example? can steps to do it? thanks alot ya...
Similar triangle:
Lets say you have six vectors, A, B, C, D, E, F.
Suppose ABC forms a triangle and DEF for another triangle.
Find AB, AC, BC, DE, DF and EF.
ABC is similar to DEF if AB/DE = AC/DF = BC/EF, though it is not necessary in this order.
Finding Area:
Lets say you are given three vectors X, Y and Z.
Find XY, XZ and YZ first.
Now, using Heron's formula, you will have S = 1/2 x (XY +XZ +YZ)
The area of the triangle will be sqrt ( S x (S-XY) x (S-XZ) x (S-YZ) ).
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Area questions on vectors are usually found by using the similar areas method or the same height triangle area method or a variation of the same height triangle area method by drawing a suitable parallelogram.
It is too tedious to find
vectors XY, XZ and YZ first. Next, need to find the magnitudes of vectors XY, XZ and YZ.
Then, In using Heron's formula, S = 1/2 x ( lXYl +lXZl +lYZl)
Then, find the area of the triangle by sqrt ( S x (S-lXYl) x (S-lXZl) x (S-lYZl) ).
No "O" level E.Maths students will use this method for area questions on vectors.
In addition, many areas questions on vectors asked to find the ratios of the areas only and the answer is usually found in 1 or 2 lines and there is not a need to find the actual areas of the triangles.
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Originally posted by Lee012lee:
Area questions on vectors are usually found by using the similar areas method or the same height triangle area method or a variation of the same height triangle area method by drawing a suitable parallelogram.
It is too tedious to find
vectors XY, XZ and YZ first. Next, need to find the magnitudes of vectors XY, XZ and YZ.
Then, In using Heron's formula, S = 1/2 x ( lXYl +lXZl +lYZl)
Then, find the area of the triangle by sqrt ( S x (S-lXYl) x (S-lXZl) x (S-lYZl) ).
No "O" level E.Maths students will use this method for area questions on vectors.
In addition, many areas questions on vectors asked to find the ratios of the areas only and the answer is usually found in 1 or 2 lines and there is not a need to find the actual areas of the triangles.
Pardon me for torturing a sec school student.
I am use to 'cheating' with Heron's formula, since you don't even need to know any angles or where the base/height is to find the area.
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Heron's formula should not be used for area questions on vector.
Heron's formula can only be used to find the the area of a triangle when the lengths of all 3 sides are given or calculated. In other cases, it will not be useful at all.
It is for this reason that the Heron's formula no longer appears in the "O" level E.Maths textbooks, guidebooks and formula books.