
How do vector quantities differ from scalar quantities?
Answer
495.6k+ views
Hint: Vector quantities consider the magnitude and direction
Scalar quantities consider only the magnitude
Change in vector quantities are the result of the change in any of the magnitude or direction
The change in scalar quantity only depends upon the change in magnitude.
Complete solution:
Scalar Quantities: A type of quantity in which measurement is defined only by the magnitude is known as a scalar quantity. A scalar quantity never considers the direction it is only concerned with magnitude. So, in the case of scalar, whenever a change in quantity is noted then it is only due to the variation in its magnitude.
Scalar quantities follow basic laws of algebra and thus can be easily added, subtracted, multiplied, or divided algebraically just like normal numbers. However, they must contain the same units. The multiplication of two scalar quantities is known as the dot product.
Vector Quantities: A quantity in which measurement is defined by both magnitude and direction is said to be a vector quantity. Two vector quantities are said to be equal when they have equal magnitude and similar direction. Hence, we can say that change in vector quantity is associated with variation in both magnitude and direction. As the direction is associated with the quantity, it does not follow basic algebraic laws but follows the laws of vector algebra.
Vector quantities can never be divided from one another. However, the vector product of two quantities can be produced and it is said to be the cross product.
The following chart shows the basic differences between Scalar and Vector quantities.
Note: If the initial position and final position of the object is zero then its displacement (Vector) is zero.
Distance (Scalar)covered cannot be zero.
If displacement is zero velocity will be zero.
Since distance covered cannot be zero so speed can also not be zero.
Scalar quantities consider only the magnitude
Change in vector quantities are the result of the change in any of the magnitude or direction
The change in scalar quantity only depends upon the change in magnitude.
Complete solution:
Scalar Quantities: A type of quantity in which measurement is defined only by the magnitude is known as a scalar quantity. A scalar quantity never considers the direction it is only concerned with magnitude. So, in the case of scalar, whenever a change in quantity is noted then it is only due to the variation in its magnitude.
Scalar quantities follow basic laws of algebra and thus can be easily added, subtracted, multiplied, or divided algebraically just like normal numbers. However, they must contain the same units. The multiplication of two scalar quantities is known as the dot product.
Vector Quantities: A quantity in which measurement is defined by both magnitude and direction is said to be a vector quantity. Two vector quantities are said to be equal when they have equal magnitude and similar direction. Hence, we can say that change in vector quantity is associated with variation in both magnitude and direction. As the direction is associated with the quantity, it does not follow basic algebraic laws but follows the laws of vector algebra.
Vector quantities can never be divided from one another. However, the vector product of two quantities can be produced and it is said to be the cross product.
The following chart shows the basic differences between Scalar and Vector quantities.
SCALAR QUANTITY | VECTOR QUANTITY |
Associated with magnitude only | Associated with Magnitude and direction both |
Representation: Simply by the symbol of quantity. | Representation: Either by the symbol of quantity in bold or by an arrow above the symbol of quantity. |
Dimension: One-dimensional | Dimension: Either one, two, or three-dimensional. |
Nature: Simple | Nature: Complex |
Variation: Change in quantity is only the result of magnitude variation. | Variation: Change in quantity is the outcome of variation in either magnitude, direction, or both simultaneously. |
Examples: Distance, temperature, speed, charge, frequency, etc. | Examples: Displacement, momentum, force, electric field, magnetic field, etc. |
Note: If the initial position and final position of the object is zero then its displacement (Vector) is zero.
Distance (Scalar)covered cannot be zero.
If displacement is zero velocity will be zero.
Since distance covered cannot be zero so speed can also not be zero.
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