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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 cases
- when the two vectors are in same direction, and
- when the two vectors are null vectors.
In all other cases sum of magnitudes is greater than magnitude of the sum of two vectors.
What else can I help you with?
Can the sum of the magnitudes of two vectors ever b equal to the the sum of these two vectors?
Not really. The sum of the magnitudes is a scalar, not a vector - so they can't be equal. But the sum of the two vectors can have the same magnitude, if both vectors point in the same direction.
Suppose you have two vectors that have different magnitudes can the vectors sum ever be zero?
No. The largest possible resultant magnitude is the sum of the individual magnitudes.The smallest possible resultant magnitude is the difference of the individual magnitudes.
Can the sum of of the magnitudes of two vectors ever be equal to the magnitudes of the sum of these two vectors?
Yes, the Triangle Inequality states that the sum of the magnitudes of two vectors can never be equal to the magnitude of the sum of those two vectors. Mathematically, if vectors a and b are non-zero vectors, then |a| + |b| ≠ |a + b|.
Can the sum of the magnitudes of two vectors ever be equal to the magnitudes of the sum of these two vectors?
No, the magnitudes of the sum of two vectors are generally greater than or equal to the sum of the magnitudes of the individual vectors. The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side, which applies to vector addition as well.
Can the magnitude of the difference between two vectors ever be greater than the magnitude of either vector?
Yes, the magnitude of the difference between two vectors can be greater than the magnitude of either vector. This can occur when the vectors are in opposite directions or have different magnitudes such that the resulting difference vector is longer than either of the original vectors.
Can a pair of vectors with unequal magnitudes ever add to zero?
No.
Can the magnitude if the difference between two vectors ever be greater than the magnitude of their sum?
No, the magnitude of the difference between two vectors cannot be greater than the magnitude of their sum. This is due to the triangle inequality, which states that the magnitude of the sum of two vectors is always greater than or equal to the magnitude of their difference.
Can the sum of two or three vectors ever be zero?
Yes. Two vectors that have equal magnitude and point in opposite directions have a sum of zero. (Like <1,0> and <-1,0>, one pointing in the positive x direction and one in negative x direction. The same idea applies with three vectors. For example, <1,0,0>, <-1,1,0> and <0,-1,0> have a sum of <0,0,0>.
Can the magnitude of a vector be ever equal to one of its components?
Yes. - if all the other components are zero. When the word "component" means the mutually perpendicular vectors that add (through vector addition) to form the resultant, then then answer is that "the magnitude of a vector" can equal one of its components, if and only if all other components have zero length (magnitude). This answer applies to the typical case of a vector being expressed in terms of components defined by an orthogonal basis. In normal space, these basis vectors merely define the relevant orthogonal coordinate system. There are, however, mathematical systems that use a nonorthogonal basis and the answer is different and presumably not part of the submitted question.
Has there ever been a 12.5 earthquake?
Earthquake magnitudes are typically whole numbers, measured on the Richter scale. A magnitude of 12.5 would be unprecedented and beyond the highest levels recorded by seismologists. The strongest recorded earthquake, the 1960 Valdivia earthquake in Chile, had a magnitude of 9.5.
Has there ever been an earthquake in London?
Yes, there have been earthquakes in London, although they are rare and generally have low magnitudes. The last recorded significant earthquake in London occurred in 1580 with an estimated magnitude of around 5.8.
When if ever can a vector quantity be added to a scaler quantity?
A vector quantity can never be added to a scalar quantity because they represent different types of physical quantities that cannot be directly combined in arithmetic operations. Scalars have magnitudes only, while vectors have magnitudes and directions. Adding a vector to a scalar does not result in a meaningful physical quantity.
