Question

Can we multiply two vectors?

Answer 1

To answer this question, we first need to understand what vectors are. In physics, a vector is a quantity with both magnitude and direction. It's usually represented by an arrow with the same direction as the amount and a length proportionate to the magnitude of the quantity.

Complete step-by-step solution:
Vector multiplication - Vector multiplication is a term that refers to one of various methods for multiplying two (or more) vectors with each other. It could be about any of the following.
Dot product – The dot product, also known as the scalar product, is an algebraic operation that returns a single integer from two equal-length sequences of integers (typically coordinate vectors). The dot product of the Cartesian coordinates of two vectors is commonly used in Euclidean geometry. Even though it is not the only inner product that may be defined on Euclidean space, it is frequently referred to as "the" inner product (or, more rarely, projection product) (see Inner product space for more).
${\text{A }} \cdot {\text{ B = }}|A\left| {\text{ }} \right|B|{\text{ }}cos{\text{ }}\theta$
Cross product - The cross product, often known as the vector product (and sometimes referred to as the directed area product to underline its geometric importance), is a binary operation on two vectors in three-dimensional space. The cross product of two linearly independent vectors a and b is a vector that is perpendicular to both a and b and so normal to the plane in which they are located. Mathematics, physics, engineering, and computer programming are just a few of the fields where it can be used. It is not to be confused with the dot item (projection product).
$A{\text{ \times }}B = |A||B|sin\theta \widehat {{\kern 1pt} n}$
So, we conclude that we can’t directly multiply two vectors, we can multiply them by only two methods as explained above.

Note: A scalar, also known as a scalar quantity, is a quantity that can be defined by a single element of a number field, such as a real number, and is frequently accompanied with units of measurement, such as "10 cm." In contrast, vectors, tensors, and other objects are characterized by a set of numbers that specify their magnitude, direction, and other properties.