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What is the sum of 2 vectors?
To find the sum of two vectors, you add their corresponding components together. For example, if you have two vectors A = (3, 5) and B = (2, -1), the sum would be A + B = (3 + 2, 5 + (-1)) = (5, 4).
When are magnitudes of 2 vectors added?
The magnitudes of two vectors are added when calculating the resultant magnitude of their vector sum. This can be done using the Pythagorean theorem, where the magnitude of the resultant vector is the square root of the sum of the squares of the magnitudes of the individual vectors.
What does the addition of 2 vectors give you?
Adding two vectors results in a new vector that represents the combination of the two original vectors. The new vector is defined by finding the sum of the corresponding components of the two vectors.
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|.
Is it possible to add any 2 vectors?
Yes, it is possible to add any two vectors as long as they have the same number of dimensions. The result of adding two vectors is a new vector whose components are the sum of the corresponding components of the original vectors.
What is the sum of 2 vectors?
To find the sum of two vectors, you add their corresponding components together. For example, if you have two vectors A = (3, 5) and B = (2, -1), the sum would be A + B = (3 + 2, 5 + (-1)) = (5, 4).
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.
Can the sum of 2 vectors be 0 if they are of unequal magnitude?
It is impossible if the two vectors are of unequal magnitude.
When Two vectors have unequal magnitude can their sum be zero explain reason?
No two vectors of unequal magnitude cannot give the sum 0 because for 0 sum the 2 vectors must be equal and in opposite direction
When adding two vectors at right angles is the resultant of the vectors the algebraic sum of the two vectors?
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
What is the sum of two or more vectors added together called?
The sum of any number of vectors is itself a vector, just as the sum of any number of scalars (normal numbers) is a normal number.If a vector is resolved into 2 components, x and y, in the form [x,y], then it can be added to any other vector resolved into 2 components [z,a].[x,y]+[z,a]=[x+z,y+a]
What is the longest and the shortest that the sum of two unit vectors can be?
The longest sum of two unit vectors occurs when they are aligned in the same direction, resulting in a maximum magnitude of 2. Conversely, the shortest sum occurs when the two unit vectors are directly opposite each other, yielding a minimum magnitude of 0. Thus, the sum can range from 0 to 2.
When are magnitudes of 2 vectors added?
The magnitudes of two vectors are added when calculating the resultant magnitude of their vector sum. This can be done using the Pythagorean theorem, where the magnitude of the resultant vector is the square root of the sum of the squares of the magnitudes of the individual vectors.
What are vectors and what are the 2 properties of them?
Vectors are quantities that have a value as well as a direction.Vector addition is commutative: x + y = y + xThe value of the sum of two vectors is always less than or equal to the sum of their individual values.|x + y| ≤ |x| + |y|
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 does the addition of 2 vectors give you?
Adding two vectors results in a new vector that represents the combination of the two original vectors. The new vector is defined by finding the sum of the corresponding components of the two vectors.
What is the sum of the measures of 1 2 3 and 4?
10, unless they are non collinear vectors.
