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Because scalars do not take in the direction but just the magnitude while vectors can. You can add vectors ONLY if they are in the same direction.

Q: Why can't we add or subtract vectors like scalars?

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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).

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]

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).

You add or subtract only the numerators

no, to add and subtract like and unlike fractions the denominator has to be the same,

Related questions

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.

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

In base 10 and above: Yes(if you are dividing commutative things like scalars (numbers) but not if you have vectors.)

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.

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).

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]

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).

Scalars are quantities that have only magnitude, such as temperature or mass. Vectors are quantities that have both magnitude and direction, such as velocity or force. Scalars can be added or subtracted just like numbers, while vectors require consideration of their direction as well.

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 .

To subtract vectors, you can simply reverse the direction of the vector you are subtracting (by multiplying it by -1) and then add it to the original vector using vector addition. This process results in the difference vector, which represents the vector between the two initial vectors.

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..

Subtract the numerators as we normally subtract them and then divide the resultant by the denominator. It's just simple like that.