Vector And Scalar Mathematics Pdf

Mass volume energy money a vector is a quantity which has both magnitude and direction.

Vector and scalar mathematics pdf. The scalar multiplication of a vector satisfies the distributive laws. M n a mn a n m a 2. Direction is that of vector or opposite to vector. According as k is positive or negative resp.

Properties of multiplication of vectors by scalars. I ii multiplying a vector by a scalar if v is a nonzero vector and c is a nonzero scalar we define the product of c and v. Vector multiplication 2 1 scalar product 2 1 1 properties of scalar product 2 1 2 angle between two vectors 2 2 vector product 2 2 1 properties of vector products 2 2 2 vector product of unit vectors 2 2 3 vector product in components 2 2 4 geometrical interpretation of vector product 2 3 examples 2. Scalar fields vector fields and covector fields first we study scalar fields.

Vector addition and subtraction. The scalar multiplication of a vectors satisfies. The cartesian or rectangular component form of a vector. Then the vector from the terminal point of v to the terminal point of u is the vector u v.

F x is the altitude at the location x. By a scalar field here we mean a scalar valued function y f x with x x1 x2 xn as a point varying in the space rn. What are scalars and vectors. The magnitude of a vector is a scalar.

Scalars and vectors scalars and vectors a scalar is a number which expresses quantity. In particular and are opposite vectors. Displacement velocity acceleration electric field. Scalars may or may not have units associated with them.

Scalars and vectors. Ii position u and v so that their initial points coincide. Imagine yourself traveling in a jeep in a mountainous country with f as its height function.