define vector product .Give its properties and two examples
Answers
Answer:
the product of two real vectors in three dimensions which is itself a vector at right angles to both the original vectors. Its magnitude is the product of the magnitudes of the original vectors and the sine of the angle between their directions.
Vector product two vectors is always a vector.
Vector product of two vectors is noncommutative. ...
vector product obeys the distributive law of multiplication.
Example:- If a · b = 0 and a ≠ o, b ≠ o then the two vectors are parallel to each other.
An example for the vector product in physics is a torque (a moment of a force - a rotational force). The force applied to a lever, multiplied by its distance from the lever's fulcrum O, is the torque T, as is shown in the diagram.
Cross product (or) Vector product Cross product of two vectors is vector Its magnitude is equal to the product of their magnitudes and sino of the angle between them and the direction is perpendicular to both the vectors.
vec R = vec A * vec B = (AB * sin theta) hat n .
Where is unit vector.
E * 1 The cross product of position vector - F and force vector vec k give torque
H-h
k_{s}
B
F_{c}
C
overline tau = overline r * overline F
E * 2 The cross product of position vector and linear momentum
gives angular momentum.
vec L = vec r * vec P
GROUND
Properties
1. Cross product does not obey commutative law overline A * overline B pm overline B * overline A 2. Cross product obey's distributive law overline A *( overline B + overline C )= overline A * overline B + overline A * overline C
r = rF
(P)
3. Cross product of two parallel vectors is a null vector ie*theta = 0 deg vec A * vec B = AB sin emptyset=0 4 Cross product of two perpendicular vectors is Ax B= AB sin 90° = AB (0-90°)
5. If i, j and k are mutually perpendicular unit vectors along x, y and = axes, then
hat i × hat i = hat j × hat j = hat k × hat k = hat 0
hat i × hat j = hat k , hat j × hat k = hat i , hat k × hat i = hat j