write three properties of cross product and dot product ?
Answers
Answer:
Properties of the Cross Product:
The length of the cross product of two vectors is.
The length of the cross product of two vectors is equal to the area of the parallelogram determined by the two vectors (see figure below).
Anticommutativity:
Multiplication by scalars:
Distributivity:
The scalar triple product of the vectors a, b, and c:
Explanation:
DOT Products: (1) It is a product of the COMPONENT of one vector along the direction of the other vector. (2) The product is a SCALAR and therefore has no DIRECTION. (3) In the DOT PRODUCT of vectors A . B the scalar measure of the product is the product of the magnitudes A & B and the COSINE of the angle between them. Example: work done by a force of 50 N along a displacement of 6 meters at an angle 60 degrees:
W = F . s = F * s cos 60 = 50 * 6 * 0.5 = 150 J [Note that energy is a scalar.]
The diagram below illustrates the above three properties (courtesy of betterexplained)
Answer:
Characteristics of cross product are: (i) Cross product of two vectors is anti commutative. (iii)Cross product of two parallel vectors is zero. (iv) Cross product of two vectors is equal to the area of parallelogram formed by two vectors.