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The angle between 2 vectors can have any value.
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What is the magnitude of the resultant vectors when the angle between them is 60 degrees?
What about the two vectors? Are they of same magnitude? If so then the resultant is got by getting the resolved components. Here we need adjacent components. F cos30 + F cos30 = 2 F cos 30 = ./3 F If forces of different magnitude then we use R = ./ (P^2 + Q^2 + 2 P Q cos 60)
When displacement have the opposite derection what do you do to determine the magnitude?
Displacement is a vector quantity. Hence, while finding resultant vector we need to use vector algebra and the properties of vectors. If the 2 displacement vectore are in opposite directions,it means that the angle between them is 180degrees and hence we can directly subtract them.
What does the addition of 2 vectors give you?
a resultant vector
Is it possible to combine 2 equal vectors to give a zero resultant?
With equal angles between them - which in this case results in 360° / 3 = 120° separation between the angles.
What is the result resultant acceleration?
Acceleration is a vector, meaning each acceleration has both magnitude and direction. The resultant of vectors is basically the net acceleration on the object expressed as a single vector. For example, if there are two vectors each with a magnitude of 2 meters/(seconds squared) acting on an object and these vectors were placed on the x and y axes then you could represent this system of 2 vectors 90 degrees apart each with a magnitude of two meters/(seconds squared) as one vector of 45 degrees with a magnitude of 2 times the square root of 2 meters/(seconds squared).
How angle between vectors affects the resultant?
The Law of Cosines shows the affect of the angle between vectors. R^2 = (A+B)(A +B)*= (AA* + BB* + 2ABcos(AB)) If the angle is less than 90 degrees the resultant squared R^2 is greater than the sum of the vectors squared. If the angle is 90 degrees the resultant squared is the sum of the vectors squared. If the angle is greater than 90 degrees, the resultant squared is less than the Sum of the vectors squared.
What is the angle between 2 vectors when their sum is maximum?
180 degrees* * * * *The exact opposite!Maximum = 0 degrees, minimum = 180 degrees.
What is it when two vectors' dot product is one?
That fact alone doesn't tell you much about the original two vectors. It only says that (magnitude of vector-#1) times (magnitude of vector-#2) times (cosine of the angle between them) = 1. You still don't know the magnitude of either vector, or the angle between them.
The resultant between 2 vectors can be found by placing the vectors?
ma0!
How do you find the area of a parallelogram using 2 vectors?
Given two vectors a and b, the area of a parallelogram formed by these vectors is:a x b = a*b * sin(theta) where theta is the angle between a and b, and where x is the norm/length/magnitude of vector x.
Can the scaler product of two vectors be negetiv if the answer is yes provid a proof and given exampl?
Yes, for example the vectors <1, 0> and <-1, 0>. In general, if the angle between the two vectors is more than 90 degrees (or pi/2 radians), the scalar product is negative.
Can the sum of magnitudes of two vectors ever be equal to the magnitude of the sum of these two vectors?
Sure, if the two vectors point in the same direction.When we need the sum of magnitudes of two vectors we simply add the magnitudes, but to get the magnitude of the sum of these two vectors we need to add the vectors geometrically.Formula to find magnitude of the sum of these two vectors is sqrt[ |A|2 +|B|2 +2*|A|*|B|*cos(z) ] where |A| and |B| are magnitudes of two A and B vectors, and z is the angle between the two vectors.Clearly, magnitude of sum of two vectors is less than sum of magnitudes(|A| + |B|) for all cases except when cos(z)=1(for which it becomes = |A| + |B| ). Cos(z)=1 when z=0, i.e. the vectors are in the same direction(angle between them is 0).Also if we consider addition of two null vectors then their sum is zero in both ways of addition.So, we get two caseswhen the two vectors are in same direction, andwhen the two vectors are null vectors.In all other cases sum of magnitudes is greater than magnitude of the sum of two vectors.
1 For the two vectors find the scalar product AB and the vector product?
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
What is the dot product of two perpendicular vectors vector a and vector b respectively?
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
What is the magnitude of the resultant vectors when the angle between them is 60 degrees?
What about the two vectors? Are they of same magnitude? If so then the resultant is got by getting the resolved components. Here we need adjacent components. F cos30 + F cos30 = 2 F cos 30 = ./3 F If forces of different magnitude then we use R = ./ (P^2 + Q^2 + 2 P Q cos 60)
What are the conditions for maximum and minimum sum or resultant of two vectors?
We have 2 vectors: AC, BD. Then |AC| = a and |BD|=b (i want to make it easier) and sum i'll call s , where s = AC + BD (we're adding vectors) there is an equation: s2 = a2 + b2 - 2ab cos x , where x is an angle between vectors a and b. The sum has a maximum value when x = 0 and the minimum value when x=180*=pi (rad)
Two equal forces have their resultant equal to either at what angle are they inclined?
Let θ be the angle between the two vectors A and B such that, |A| = |B|. Therefore, R 2 = A 2 + B 2 + 2AB cosθ => A 2 = A 2 + A 2 + 2(A)(A) cosθ [since, |A| = |B| = |R|] => A 2 = 2A 2 + 2A 2 cosθ => cosθ = -1/2 => θ = 60 degrees negative sign is not considered becaus eof the modulus sign
