Question

The magnitude of the vector product of two vectors \[\left|A \right|\] and \[\left|B \right|\] maybe ?
A. Greater than AB
B. Equal to AB
C. less than AB
D. equal to 0

Answer 1

Hint: Various types of vectors are defined in vector algebra, and various operations such as addition, subtraction, product, and so on can be performed on these vectors. \[a\times b\]denotes the vector product of two vectors, \[a\] and \[b\]. Its resulting vector is perpendicular to the lines \[a\] and \[b\]. Cross products are another name for vector products.

Complete answer:
\[A\times B\] denotes the vector product or cross product of two vectors \[A\] and \[B\], and the resultant vector is perpendicular to the vectors \[A\] and \[B\]. The cross product is mostly used to find the vector that is perpendicular to the plane surface spanned by two vectors, whereas the dot product is used to find the angle between two vectors or the vector's length.

The result of combining two vectors, say\[A\times B\], is equal to another vector at right angles to both, and it happens in the three dimensions. We can use properties to find the cross-product of two vectors. Properties such as anti-commutative property and zero vector property are critical in determining the cross-product of two vectors. Other properties besides these include Jacobi property and distributive property.

Since there are two types of vector multiplications, the scalar product and the vector product have been defined. \[A\times B=~{{A}_{x}}{{B}_{x}}+{{A}_{y}}{{B}_{y}}+{{A}_{z}}{{B}_{z}}\]The scalar product of two vectors \[A\] and \[B\] is the product of the magnitudes of the two vectors and the cosine of the smallest angle between them.As a result, it could be equal, smaller, or zero.

Thus, the answer is an option A,C and D.

Note:The dot product, also known as the scalar product in mathematics, is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. The dot product of two vectors' Cartesian coordinates is widely used in Euclidean geometry. It is frequently referred to as "the" inner product (or, less frequently, projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space.