What is scalar multiplication and vector multiplication of vector quantity?

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Multiplication of vectors

When two vector quantities are multiplied, the product is sometimes a scalar quantity and sometimes a vector quantity. Based on this characteristic of the product, the product of the vector equation is divided into two parts.

1. Scalar multiplication or dot multiplication

2. Vector multiplication or cross multiplication

Scalar multiplication or dot multiplication

If we multiply two vector quantities and the product is a scalar quantity, this product is called a scalar product. To denote scalar multiplication we use the dot symbol as the symbol of multiplication, so scalar multiplication is also called dot multiplication.

Eg: Both force and displacement are vector quantities. By multiplying them scalar we get work, which is a scalar expression.

Vector multiplication or cross multiplication

If we multiply two vector quantities and the product is a vector quantity, we call it vector multiplication. Vector multiplication is also called cross multiplication because we use the cross sign as the sign of multiplication to denote vector multiplication.

For example, the radius of gyration and linear momentum are both vector quantities. By vector multiplying them we get angular momentum which is a vector quantity.