prove-that-vector-scalar-vector-

Question Number 207812 by Davidtim last updated on 27/May/24

p r o v e t h a t \frac{v e c t o r}{s c a l a r} = v e c t o r

Answered by A5T last updated on 27/May/24

L e t s c a l a r = λ \in R; a n d v e c t o r, a = (a_{1}, a_{2}, \dots, a_{n}) \in R_{n}

w h e r e e a c h a_{i} \in R . B y d e f i n i t i o n,

\frac{1}{λ} a = (\frac{a_{1}}{λ}, \frac{a_{2}}{λ}, \dots, \frac{a_{n}}{λ}) . S i n c e e a c h \frac{a_{i}}{λ} a l s o \in R, \frac{a}{λ} i s

a v e c t o r .

Commented by Davidtim last updated on 26/Oct/24

b u t w h e n w e f i n d t h e w o r k w e f o l l o w t h i s

W = F \cdot d

w h y h e r e t h e w o r k i s s c a l a r ?

Commented by A5T last updated on 26/Oct/24

T h e m a t h e m a t i c a l i d e a o f v e c t o r s / s c a l a r s i s

d i f f e r e n t f r o m t h a t i n p h y s i c s .

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