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Showing that the scalar product between all pairs of them is equally zero.
Two vector are orthogonal (or perpendicular) if the scalar product between them is zero. Lets see an example in 2D:
If we have two vector, a = (a1, a2) and b = (b1,b2), if
a · b = sqrt(a1*b1 + a2*b2) = 0
then a and b are orthogonal.
To do the same with three vector (a, b, c) you have to show that all the combinations give zero, i.e.,
a · b = a · c = b · c= 0
(as the scalar product is commutative, you only need to probe this three cases).
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∙ 14y ago
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What is the Smallest magnitude of sum of 4 and 3 meter vectors?
The smallest magnitude resulting from the addition of vectors with individual magnitudes of 4 and 3 is 1, obtained when the directions of the two component vectors are 180 degrees apart.
Is it possible to add three vectors of equal magnitudes and get zero?
Of course it is! for example, [1, √3] + [-2, 0] + [1, - √3 ] = [0, 0]. Like this example, all other sets of such vectors will form an equilateral triangle on the graph.. Actually connecting the endpoints of the 3 vectors forms the equilateral triangle. The vectors are actually 120° apart.
What are 3 measurements of vectors?
2 inches, 3 inches, and 4 inches
When two nonzero vectors A and B are added and the sum has magnitude 3 it's possible that A equals B equals 3?
The vectors can not be both equal, but they can have the same magnitude of 3, if they are at a 60 degree angle.
What is the difference between coplanar vectors and collinear vectors?
The term collinear is used to describe vectors which are scalar multiples of one another (they are parallel; can have different magnitudes in the same or opposite direction). The term coplanar is used to describe vectors in at least 3-space. Coplanar vectors are three or more vectors that lie in the same plane (any 2-D flat surface).
How do you add vectors using the component method?
1) Separate the vectors into components (if they are not already expressed as components). 2) Add each of the components separately. 3) If required, convert the vectors back to some other form. For twodimensional vectors, that would polar form.
What is the resultant of a 3 unit vector and 4 unit vector at right angles to each other?
The multiplicative resultant is a three unit vector composed of a vector parallel to the 3 unit vector and a vector parallel to the product of the 3 unit and 4 unit vectors. R = (w4 + v4)(0 +v3) = (w40 - v4.v3) + (w4v3 + 0v4 + v4xv3) R = (0 - 0) + w4v3 + v4xv3 as v4.v3 =0 ( right angles or perpendicular)
How do you do dot product of the vectors at any dimension?
You do the dot product of the vectors by multiplying their corresponding coordinates and adding them up altogether. For instance: <1,2,3> ∙ <-3,4,-1> = 1(-3) + 2(4) + 3(-1) = -3 + 8 - 3 = 2
If a set of vectors spans R3 then the set is linearly independent?
No it is not. It's possible to have to have a set of vectors that are linearly dependent but still Span R^3. Same holds true for reverse. Linear Independence does not guarantee Span R^3. IF both conditions are met then that set of vectors is called the Basis for R^3. So, for a set of vectors, S, to be a Basis it must be:(1) Linearly Independent(2) Span S = R^3.This means that both conditions are independent.
Can three parallel vectors of uneven magnitude add to zero?
Yes - if you accept vectors pointing in opposite directions as "parallel". Example: 3 + 2 + (-5) = 0
What is the Minimum number of vectors with unequal magnitudes whose vector sum can be zero?
-- A singe vector with a magnitude of zero produces a zero resultant.-- Two vectors with equal magnitudes and opposite directions produce a zero resultant.
Is it possible to add three vectors of equal magnitude but different directions to get a null vectors?
yes, as long as they have 120 degrees separating them from each other, (360/3). all vectors must have total x and y component values of 0.
