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Vectors have a direction associated with them, scalars do not.
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How do you prove that the diagonals of a rectangle are congruent using vectors?
If the vectors emanting from one corner of the rectangel are called a and b then. (a) + (b) = one diagonal (a) + (-b) = the other diagonal and |(a) + (b)| = |(a) + (-b)| (the absolute value of the diagonal's scalars are equal)
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors?
Magnitude? Yes. Simple answer: think of it as a triangle. Can a triangle have three sides of the same length? Yes. Long answer: there really isn't a long answer. To get the resultant of two vectors, one would add up the components of each vector. While it is impossible to add two vectors of the same magnitude and derive a resultant of the same magnitude AND DIRECTION as one of the vectors, one need only to create a directional difference of exactly 60 degrees between the first two vectors to result in a resultant of like magnitude. Math really is the most perfect language. Vectors are to triangles what optics are to to the study of conics!
Two vectors of equal magnitude have got a resultant whose magitude is equal to either one of them. Find the angle between the two vectors?
120 deg
What is the difference between zero and vector zero?
The zero vector occurs in any dimensional space and acts as the vector additive identity element. It in one dimensional space it can be <0>, and in two dimensional space it would be<0,0>, and in n- dimensional space it would be <0,0,0,0,0,....n of these> The number 0 is a scalar. It is the additive identity for scalars. The zero vector has length zero. Scalars don't really have length. ( they can represent length of course, such as the norm of a vector) We can look at the distance from the origin, but then aren't we thinking of them as vectors? So the zero vector, even <0>, tells us something about direction since it is a vector and the zero scalar does not. Now I think and example will help. Add the vectors <2,2> and <-2,-2> and you have the zero vector. That is because we are adding two vectors of the same magnitude that point in opposite direction. The zero vector and be considered to point in any direction. So in summary we have to state the obvious, the zero vector is a vector and the number zero is a scalar.
Can the sum of two vectors be equal to either of the vectors explain?
Yes, if one of the vectors is the null vector.
Are vectors and scalars the same?
No, scalars and vectors are not the same. Scalars are measurements in numbers. Examples: work, energy, mass, speed, and distance. Scalars measure in one magnitude. Vectors measure velocity, acceleration, force, and momentum.
Why is it important to know the difference between vectors and scalar?
Scalar quantity is the usual one. It is already there unavoidable. But vector is the new one. Why do we need it? Suppose say two persons by name John and Johann push a box with forces 4N and 3N, what could be the effective force on the box? One may say 7 N by adding them. One may say just 1N because of getting the difference. Another may say 5N. How? Why do they give different answers? It is because the directions in which the forces acting are considered in different ways. If both in the same, addition is ok. If in opposite then difference is right one. If they are at right angles then pythagros technique. So direction is the most essential data to get the right answer. Hence magnitude with direction is known to be vector quantity.
How do you prove that the diagonals of a rectangle are congruent using vectors?
If the vectors emanting from one corner of the rectangel are called a and b then. (a) + (b) = one diagonal (a) + (-b) = the other diagonal and |(a) + (b)| = |(a) + (-b)| (the absolute value of the diagonal's scalars are equal)
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).
What is the difference scalars and vector?
Vectors and scalars are components of complex numbers. Complex numbers are z= x + iy, with one vector iy. The difference between the scalar part x and the vector part iy is, the square of the real part x is positive x^2 and the square of the vector part iy is negative -y^2. This square rule is what distinguishes scalars from vectors. Complex and Real Numbers are a subset of Quaternion Numbers.thrQuaternion q=w + ix + jy + kz = qw + qv contains one scalar (qw=w) andthree vectors (qv=Ix +jy + kz), . The three vectors make for a different rule for multiplication.When there is only one vector the rule for multiplication is called commutative and AB=BA. This rule is what is generally taught in mathematics and science. Howver when there is more than one vector like in real world mathematics and science AB does not equal BA. This is called Non-commutaive mathematics.Non-commutaive mathematics is the mathematics of of Quantum Physics. Quaternions provide the Unification of Relativity and Quantum Theory. Quaternions provide the correct four dimensions of Relativity Theory and the Non-Commutativity of Quantum Theory.The general rule for multiplication of quaternionsAB= (AwBw -Av.Bv) + (AwBv + AvBw + AvxBv)If the vectos Av and Bv are parallel AvxBv is zero and multiplication is commutative. If there is only one vector i like in complex numbers then AvXBv is always parallel ixi=0.If the vectors Av and Bv are not parallel then multiplication is non-commutitive. Guess what most of the time things are not parallel in math and physics.Scalars and vectors are very different and make up the two parts of numbers in math and science. Quaternions are the only kinds of numbers that can provide unique ( associative (AB)C = A(BC) ) division, such that you can solve equations like Ax=B.Quaternion multiplication is all around us. Riding a bycycle uses quaternion math just like a gyroscope. Rotations in space requires quaternion multiplication.It is important to distinguish between scalars and vectors and time to learn quaternion mathematics and understand the real world..
When are vectors said to be perpendicular?
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors?
Magnitude? Yes. Simple answer: think of it as a triangle. Can a triangle have three sides of the same length? Yes. Long answer: there really isn't a long answer. To get the resultant of two vectors, one would add up the components of each vector. While it is impossible to add two vectors of the same magnitude and derive a resultant of the same magnitude AND DIRECTION as one of the vectors, one need only to create a directional difference of exactly 60 degrees between the first two vectors to result in a resultant of like magnitude. Math really is the most perfect language. Vectors are to triangles what optics are to to the study of conics!
What is the possibility when magnitudes of dot and cross products are equal?
if any one of the vectors is a null vector or if A is the angle between the two vectors then tanA =1
Two vectors of equal magnitude have got a resultant whose magitude is equal to either one of them. Find the angle between the two vectors?
120 deg
What is the difference between vectors and arrays?
The abstraction are the same. However, the array may be of any objects, while a vector, in narrowed definition, each element is a scalar value (e.g, int, float, double, etc), to fulfill the abs(vector) = aScalarValue property of a vector. An array with the same data type would look exactly the same. But an array of Persons will be difficult to be a vector!
What is the difference between zero and vector zero?
The zero vector occurs in any dimensional space and acts as the vector additive identity element. It in one dimensional space it can be <0>, and in two dimensional space it would be<0,0>, and in n- dimensional space it would be <0,0,0,0,0,....n of these> The number 0 is a scalar. It is the additive identity for scalars. The zero vector has length zero. Scalars don't really have length. ( they can represent length of course, such as the norm of a vector) We can look at the distance from the origin, but then aren't we thinking of them as vectors? So the zero vector, even <0>, tells us something about direction since it is a vector and the zero scalar does not. Now I think and example will help. Add the vectors <2,2> and <-2,-2> and you have the zero vector. That is because we are adding two vectors of the same magnitude that point in opposite direction. The zero vector and be considered to point in any direction. So in summary we have to state the obvious, the zero vector is a vector and the number zero is a scalar.
What is the difference between one and one's?
difference between one- ones
