In simple terms, a scalar is a quantity such as temperature, pressure, density, mass, energy etc. which can be quantified with a single number. That is, a scalar has a magnitude but no direction.
Similarly, a vector is a quantity such as displacement, velocity, force, electric field etc. which has not only a magnitude but also a direction in space.
Scalars, being ordinary numbers, can be added together, multiplied etc. in the normal way.
The algebra of vectors is a little more complex:
(1) Given two vectors a and b, we can form the sum a + b using the parallelogram law (see the related links).
(2) Given a vector a and a scalar k, we can multiply them to obtain a new vector ka having the same (or directly opposite) direction as a, but with its length multiplied by k. (Note: if k is negative then the new vector's direction is opposite to a's; otherwise the directions are the same.)
(3) Given two vectors, we can form their scalar producta⋅b (also known as the dot product). This is a scalar value, given by the product of the vectors' magnitudes with the cosine of the angle between them. Equivalently, the scalar product is the magnitude of the first vector multiplied by the length of the projection of the second vector onto the first.
(4) Given two vectors, we can also form their vector product a×b (also known as the cross product). This is a vector at right angles to both the original vectors, having a magnitude equal to the product of the original vectors' magnitudes with the sine of the angle between them. There is a subtlety here involving handedness; see the related links for more information.
All of the above operations have practical uses in physics, particularly in Newtonian mechanics and classical electromagnetism.
A scalar quantity only has magnitude (how much). Like Mass. A vector quantity has magnitude and direction. Like Force.
An object being pushed upwards by one Newton of force and from the side by two Newtons of force, for example, might be illustrated with one vector arrow pointing upward from the center of the object and another, twice as long, pointing from the center of the object to the side. Such illustrations are invaluable in physics, because they allow one to apply mathematics (trigonometry, in this case) to determine the resulting force (scalar) and direction (vector).
No, a scalar quantity cannot be the product of two vector quantities. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. When two vectors are multiplied, the result is a vector, not a scalar.
Vector quantities have both magnitude and direction, such as velocity and force. Scalar quantities have only magnitude and no specific direction, such as speed and temperature.
No, a vector quantity and a scalar quantity are different. A vector has both magnitude and direction, while a scalar has only magnitude. Velocity and force are examples of vector quantities, while speed and temperature are examples of scalar quantities.
Scalar forces have only magnitude, such as pressure and temperature. Vector forces have both magnitude and direction, such as force and velocity. Scalars are represented by single values, while vectors are represented by quantities with both magnitude and direction.
Work and energy are scalar quantities because they have magnitude but no direction. They are described by a single numerical value rather than having both magnitude and direction like vector quantities.
No, a scalar quantity cannot be the product of two vector quantities. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. When two vectors are multiplied, the result is a vector, not a scalar.
Scalar quantities - quantities that only include magnitude Vector quantities - quantities with both magnitude and direction
Scalar quantities are defined as quantities that have only a mganitude. Vector quantities have magnitude and direction. Some example of this include Scalar Vector Mass Weight length Displacement Speed Velocity Energy Acceleration
Scalar and vector quantities are both used in physics to describe properties of objects. They both have magnitude, which represents the size or amount of the quantity. However, the key difference is that vector quantities also have direction associated with them, while scalar quantities do not.
A vector is characterized by having not only a magnitude, but a direction. If a direction is not relevant, the quantity is called a scalar.
Vector quantities have both magnitude and direction, such as velocity and force. Scalar quantities have only magnitude and no specific direction, such as speed and temperature.
No, a vector quantity and a scalar quantity are different. A vector has both magnitude and direction, while a scalar has only magnitude. Velocity and force are examples of vector quantities, while speed and temperature are examples of scalar quantities.
No. Force and acceleration are vector quantities.
Scalar and vector quantities are both used to describe physical quantities in physics. The key similarity between them is that they both involve numerical values. However, vector quantities also have a direction associated with them, while scalar quantities do not.
Scalar forces have only magnitude, such as pressure and temperature. Vector forces have both magnitude and direction, such as force and velocity. Scalars are represented by single values, while vectors are represented by quantities with both magnitude and direction.
Work and energy are scalar quantities because they have magnitude but no direction. They are described by a single numerical value rather than having both magnitude and direction like vector quantities.
scalar quantities have magnitude only while vector quantities have both magnitude and direction. e.g.s of scalar quantities- distance, mass, temperature, speed e.g.s of vector quantities-displacement, velocity, acceleration, weight, force