Vectors have the magnitude and direction, scalars have only magnitude. Addition of vectors A and B will produce a vector C. Such that C=A+B. C is a vector because it will have magnitude and the direction.
For an example consider a moving sidewalk such as those in the airports. If such a sidewalk is moving South at 2 miles per hour, its velocity is vector A. If a person walking on that sidewalk at 3 miles per hour also South, that persons velocity is vector B. However, that person will be moving at 2+3=5 miles per hour in relation to a stationary observer or in other words with the velocity of vector C.
Further, consider A+B1=C1.
If that person is walking North, or the opposite direction of treadmill's (if he or she got on the wrong sidewalk :) ), that person's velocity will be -3 miles per hour that will be vector B1. Thus in relation to a stationary observer that person is moving 2+(-3)=(-1) miles per hour towards South, the velocity of vector C1. That is the person is moving North at 1 mile per hour.
Scalar addition involves adding a scalar quantity to each element of a vector. This is done by adding the scalar to the magnitude of the vector without changing its direction. The result is a new vector that represents the original vector displaced by the magnitude of the scalar in the same direction.
A scalar quantity added to a vector quantity is a complex quantity. An example is a complex number z = a + ib, a is the scalar and ib is the vector quantity.If the vector quantity is 3 dimensional, ib + jc + kd, then the scalar and vector forms a quaternion quantity.
Vector quantities can be added and subtracted using vector addition, but they cannot be divided like scalar quantities. However, vectors can be multiplied in two ways: by scalar multiplication, where a scalar quantity is multiplied by the vector to change its magnitude, or by vector multiplication, which includes dot product and cross product operations that result in a scalar or vector output.
The product of scalar and vector quantity is scalar.
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
Scalar addition involves adding a scalar quantity to each element of a vector. This is done by adding the scalar to the magnitude of the vector without changing its direction. The result is a new vector that represents the original vector displaced by the magnitude of the scalar in the same direction.
A scalar quantity added to a vector quantity is a complex quantity. An example is a complex number z = a + ib, a is the scalar and ib is the vector quantity.If the vector quantity is 3 dimensional, ib + jc + kd, then the scalar and vector forms a quaternion quantity.
Vector quantities can be added and subtracted using vector addition, but they cannot be divided like scalar quantities. However, vectors can be multiplied in two ways: by scalar multiplication, where a scalar quantity is multiplied by the vector to change its magnitude, or by vector multiplication, which includes dot product and cross product operations that result in a scalar or vector output.
The product of scalar and vector quantity is scalar.
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
Moment arm is a scalar quantity, as it represents the perpendicular distance from the axis of rotation to the line of action of a force. It does not have a direction associated with it, unlike vectors.
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 is NOT a scalar. The two (vector and scalar) are different things. A vector is a quantity (measurement) in which a direction is important. A scalar is a quantity in which a direction is NOT important.
A vector quantity includes a direction; a scalar does not.A vector quantity includes a direction; a scalar does not.A vector quantity includes a direction; a scalar does not.A vector quantity includes a direction; a scalar does not.
A vector has direction, where as a scalar does not. When you add two vectors, it is like you are moving one vector to the end of the other vector, and closing off the triangle with a vector for the third side. That third vector is the addition of the first two vectors. The new vector points in a specific direction, so it cannot be a scalar.
Scalar product (or dot product) is the product of the magnitudes of two vectors and the cosine of the angle between them. It results in a scalar quantity. Vector product (or cross product) is the product of the magnitudes of two vectors and the sine of the angle between them, which results in a vector perpendicular to the plane containing the two original vectors.
The resultant of two vectors cannot be a scalar quantity.