Answer to Question #259571 in Analytic Geometry for Almas

Question

Prove and Disprove that a scalar and vector can be added.

Answer 1

let $\overrightarrow{V}=<V_1,V_2>$

where V₁ and V_{2 a} are vectors.

let K be the scalar

A vector and scalar can be multiplied but cannot be added or substracted.

scalar multiplication

$\overrightarrow{V}=K<V_1,V_2>\\<KV_1,KV_2>$

after scalar multiplication

vector addition

let

$\overrightarrow{V}=<V_1,V_2>\\\overrightarrow{U}=<U_1,U_2>\\\overrightarrow{V}+\overrightarrow{U}=<V_1+U_1,V_2+U_2>$

scalar multiplication and vector addition

$\overrightarrow{KV}=<KV_1,KV_2>\\\overrightarrow{KU}=<KU_1,KU_2>\\K(\overrightarrow{V}+\overrightarrow{U})=<K(V_1+U_1),K(V_2+U_2)>$

scalar and vector addition

consider a vector $\overrightarrow{v}$

which looks like

consider a scalar k

let say k=5

we cannot add a number to a vector