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What are scalars?
A measurement without direction, meaning that it is only a magnitude (as opposed to vector which has magnitude and direction). E.g, a speed of 5km/h is a scalar while a velocity of 19m/s west is a vector.Scalars are a type of number that have size (but not direction like vectors).
Can you add vector like scalars or not?
No. Because vectors have direction as well as magnitude, you must take the direction into account when you add them. Example: Vector A parallel to [0,0; 0,4] Vector B parallel to [0,0; 3,0] These vectors are at right angles to each other Vector A has a magnitude of 4, Vector B an magnitude of 3. A + B = has a magnitude of 5, parallel to [0,0;3,4]
What are the method in adding vector?
The method in adding vectors is "add like components to likes".For example A= Ia1 + Ja2 + Ka3 and B= Ib1 + Jb2 + Kb3 added is :A+B= I(a1 +b1) + J(a2 + b2) + K(a3 + b3).I, J and K are the vector components.Physics really involves vectors V and scalars S called Quaternions Q=S +V.The method is the same but now likes include vectors and scalars.Q1 + Q2 = (S1 +S2) + (V1 + V2).
How do you add and subtract like denominator?
You add or subtract only the numerators
Do you add and subtract like and unlike fractions in the same way?
no, to add and subtract like and unlike fractions the denominator has to be the same,
Are scalers negative why?
Scalars are not always negative. The word scalar means that a value behaves like the numbers we are familiar with. You just add and subtract them. These are different than vectors, where you need to break them into scalars in order to add them first.
How do you subtract vectors?
it depends on the method of subtraction. If the vectors are drawn graphically then you must add the negative of the second vector (same magnitude, different direction) tail to tip with the first vector. If the drawing is to scale, then the resultant vector is the difference. If you are subtracting two vectors <x1, y1> - <x2, y2> then you can subtract them component by component just like scalars. The same rules apply to 3-dimensional vectors
How do you classify physical quantities?
Physical quantities can be classified as scalars or vectors. Scalars have only magnitude, such as mass or temperature, while vectors have both magnitude and direction, like velocity or force. Scalars and vectors are further categorized into base quantities (e.g. length, time) and derived quantities (e.g. speed, acceleration).
Why are vectors considered to be vectors?
Vectors are considered vectors because they have both magnitude (size or length) and direction. This property distinguishes vectors from scalars, which only have magnitude. In physics and mathematics, vectors are essential for representing physical quantities like force, velocity, and displacement that have both size and direction.
Is 10 divided by 4 equal to 5 divided by 2?
In base 10 and above: Yes(if you are dividing commutative things like scalars (numbers) but not if you have vectors.)
What is the difference between scalars and vectors using displacement and distance?
Displacement is a vector quantity that represents the change in position of an object in a specific direction, including magnitude and direction. Distance is a scalar quantity that represents the length of the path traveled by an object, regardless of direction. Scalars only have magnitude, while vectors have both magnitude and direction.
What are scalar relationships?
Scalar relationships refer to mathematical relationships that involve only magnitude, with no direction. They are characterized by numerical values and do not incorporate vectors or directions. Scalars can be added, subtracted, multiplied, and divided like ordinary numbers.
Can you add vector like scalars or not?
No. Because vectors have direction as well as magnitude, you must take the direction into account when you add them. Example: Vector A parallel to [0,0; 0,4] Vector B parallel to [0,0; 3,0] These vectors are at right angles to each other Vector A has a magnitude of 4, Vector B an magnitude of 3. A + B = has a magnitude of 5, parallel to [0,0;3,4]
When a quantity requires both magnitude and the direction it is classified as what quantity?
The quantity is classified as a vector. Vectors represent physical quantities that have both magnitude and direction, such as force, velocity, and acceleration. Scalars, on the other hand, only have magnitude and no direction, like mass and temperature.
What are the method in adding vector?
The method in adding vectors is "add like components to likes".For example A= Ia1 + Ja2 + Ka3 and B= Ib1 + Jb2 + Kb3 added is :A+B= I(a1 +b1) + J(a2 + b2) + K(a3 + b3).I, J and K are the vector components.Physics really involves vectors V and scalars S called Quaternions Q=S +V.The method is the same but now likes include vectors and scalars.Q1 + Q2 = (S1 +S2) + (V1 + V2).
Who gave concept of vectors and scaler?
William Rowan Hamilton, the Irish Genius came up with the concepts of Scalar and Vector in 1843 when he created Quaternions, a four dimensional number. A quaternion consists of one scalar and three vectors, Q= r + Ix + jy + Kz where (r,x, y and z) are real numbers or Scalars and (I, J and K) are Vector numbers.Unlike Scalars, Vector numbers squared are Negative: I^2=J^2=K^2=IJK= - 1.Quaternions are the only numbers that form an Associative Division Algebra, in other words the only numbers where you can uniquely solve Algebraic Equations like Ax =b .Real numbers and Complex numbers are subsets of Quaternions.Quaternions were "famous" for their non-commutative property of vectors IJ =-JI.Quantum Physics uses Quaternions non-commutativity.Physicists should always distinguish Scalars from Vectors and learn about Hamilton's Quaternions.Newton's Law of Gravitationa Energy E= -mu/r neglects the vector energy mcV of gravity.The proper Law of Gravitational Energy is Quaternion E= -mu/r + mcV .
The differences between scalar quantities and vector quantities?
Scalar quantities are represented by a magnitude only, such as time or temperature, while vector quantities have both magnitude and direction, like displacement or velocity. Scalars can be added or subtracted algebraically, whereas vectors require vector addition that considers both magnitude and direction. Scalars are also simpler to work with mathematically, while vectors require more complex operations.
