Question

A dot product is 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 #59689 – Math – Analytic Geometry

Question

A dot product is said to be distributive, if

a) $m \cdot u = u \cdot m$ ;

b) $m(u\cdot v) = v(m\cdot v);$

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

d) $m = u$

Solution

The distributivity of the dot product means that for any three vectors $u, v, w$ hold the following equality:

$$u \cdot (v + w) = (u \cdot v + u \cdot w).$$

Therefore, the correct answer is $c$ ), that is,

$$u \cdot (v + w) = (u \cdot v + u \cdot w).$$

Answer: c) $u \cdot (v + w) = (u \cdot v + u \cdot w)$ .

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