write the properties of vector product of two vector
Answers
Answer:
Properties of Vector Cross Product
1] Vector product is not commutative. That means a × b ≠ b × a
We saw that a × b = c here the thumb is pointing in an upward direction. Whereas in b × a the thumb will point in the downward direction. So, b × a = – c. So it is not commutative.
2] There is no change in the reflection.
What happens to a × b in the reflection? Suppose vector a goes and strikes the mirror, so the direction of a will become – a. So under reflection, a will become – a and b will become – b. Now a × b will become -a × -b = a × b
3] It is distributive with respect to vector addition.
This means that if a × ( b + c ) = a × b + a × c. This is true in case of addition.
Answer:
Vector product also means that it is the cross product of two vectors.
Vector product also means that it is the cross product of two vectors.Cross Product
Vector product also means that it is the cross product of two vectors.Cross ProductIf you have two vectors a and b then the vector product of a and b is c.
Vector product also means that it is the cross product of two vectors.Cross ProductIf you have two vectors a and b then the vector product of a and b is c. c = a × b
Vector product also means that it is the cross product of two vectors.Cross ProductIf you have two vectors a and b then the vector product of a and b is c. c = a × bSo this a × b actually means that the magnitude of c = ab sinθ where θ is the angle between a and b and the direction of c is perpendicular to a well as b. Now, what should be the direction of this cross product? So to find out the direction, we use the rule which we call it as the ”right-hand thumb rule”.
Vector product also means that it is the cross product of two vectors.Cross ProductIf you have two vectors a and b then the vector product of a and b is c. c = a × bSo this a × b actually means that the magnitude of c = ab sinθ where θ is the angle between a and b and the direction of c is perpendicular to a well as b. Now, what should be the direction of this cross product? So to find out the direction, we use the rule which we call it as the ”right-hand thumb rule”.Suppose we want to find out the direction of a × b here we curl our fingers from the direction of a to b. So if we curl our fingers in a direction as shown in the above figure, your thumb points in the direction of c that is in an upward direction. This thumb denotes the direction of the cross product.
Vector product also means that it is the cross product of two vectors.Cross ProductIf you have two vectors a and b then the vector product of a and b is c. c = a × bSo this a × b actually means that the magnitude of c = ab sinθ where θ is the angle between a and b and the direction of c is perpendicular to a well as b. Now, what should be the direction of this cross product? So to find out the direction, we use the rule which we call it as the ”right-hand thumb rule”.Suppose we want to find out the direction of a × b here we curl our fingers from the direction of a to b. So if we curl our fingers in a direction as shown in the above figure, your thumb points in the direction of c that is in an upward direction. This thumb denotes the direction of the cross product.While applying rules to direction, the rotation should be taken to smaller angles that is <180° between a and b. So the fingers should always be curled in acute angle between a and b.