__maths__>__Properties of Vector Arithmetics__>__Properties of Vector Multiplication by Scalar__### Multiplication by Product of Scalars

In this page, multiplication of a vector by product of scalars is explained.

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Given that `vec p = ai+bj+ck` and `lambda, mu` where `a,b,c,lambda,mu in bbb R`, What will be the result of `(lambda mu) vec p `?

- `lambda(mu vec p)`
- `lambda(mu vec p)`
- `lambda vec p mu vec p`
- `mu vec p

The answer is '`lambda(mu vec p)`'. This is proven by multiplying the components individually by the scalar.

• Multiplication of vector by a product of two scalars is equivalently multiplication by the scalars one by one.

**Multiplication by Product of scalars: **Given a scalar as product of two scalars `lambda mu`,

`(lambda mu)vec p = lambda(mu vec p)`

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