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Can the directions of the sum of two two vectors be equal to the directions of difference of two vectors?
Yes.
The sum of two vectors is a minimum when the angle between them is what?
180 degrees. Then the sum of the two vectors has a magnitude equal to the difference of their individual magnitudes.
Is it possible to find the sum of two parallel vectors using the parallelogram method?
No, it is simpler than that. Simply add the two magnitudes. The direction will be the same as the parallel vectors.
What is vector dot product?
The dot-product of two vectors is the product of their magnitudes multiplied by the cosine of the angle between them. The dot-product is a scalar quantity.
When is the vector sum equal in magnitude to the algebraic sum?
When the angle between any two component vectors is either zero or 180 degrees.
Can sum of two vectors be numeric?
No, the sum of two vectors cannot be a scalar.
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.
When is the vector sum of two quatities equal in magnitude to the scalar sum?
When all the vectors have the same direction.
Why isn't the sum of two vectors a scalar?
A vector has direction, where as a scalar does not. When you add two vectors, it is like you are moving one vector to the end of the other vector, and closing off the triangle with a vector for the third side. That third vector is the addition of the first two vectors. The new vector points in a specific direction, so it cannot be a scalar.
Why is scalar product two vectors a scalar?
Scalar product of two vectors is a scalar as it involves only the magnitude of the two vectors multiplied by the cosine of the angle between the vectors.
Is resultant a vector quantity?
The resultant of two vectors cannot be a scalar quantity.
Why the product of two vectors is sometime scalar and sometime vector?
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
What is the product of two vector quantities?
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Can the sum of the magnitudes of two vectors ever be equal to the magnitudes of the sum of these two vectors?
only if the vectors have the same direction
What is a matrix and a scalar?
A matrix and a scalar is a matrix. S + M1 = M2. A scalar is a real number whose square is positive. A matrix is an array of numbers, some of which are scalars and others are vectors, square of the number is negative. A matrix can be a quaternion, the sum of a scalars and three vectors.
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.
Does the scalar product of two vectors depend on the choice of coordinate system?
No.
