Question

A dot product said to be distributive,if. A...A....

a)m.u=u.m

b)m(u.v)=v(m.v)

c)u.(v+w)=(u.v+u.w)

d)m=u

Answer 1

Answer on Question #59655 – Math – Analytic Geometry

Question

1. A dot product said to be distributive, if:

a) $\mathbf{m} \cdot \mathbf{u} = \mathbf{u} \cdot \mathbf{m}$;

b) $\mathbf{m}(\mathbf{u} \cdot \mathbf{v}) = \mathbf{v}(\mathbf{m} \cdot \mathbf{u})$;

c) $\mathbf{u} \cdot (\mathbf{v} + \mathbf{w}) = (\mathbf{u} \cdot \mathbf{v} + \mathbf{u} \cdot \mathbf{w})$;

d) $\mathbf{m} = \mathbf{u}$.

Solution

Dot product is distributive if it satisfies:

$$\mathbf{u} \cdot (\mathbf{v} + \mathbf{w}) = (\mathbf{u} \cdot \mathbf{v} + \mathbf{u} \cdot \mathbf{w}).$$

Hence, the correct answer is c).

**Answer**: c) $\mathbf{u} \cdot (\mathbf{v} + \mathbf{w}) = (\mathbf{u} \cdot \mathbf{v} + \mathbf{u} \cdot \mathbf{w})$.

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