# Thread: scalar multiplied by a vector proof

1. ## scalar multiplied by a vector proof

Show that if c is a scalar then ||cu||=|c|||u||

let u$\displaystyle =(x_1, x_2, ..., x_n)$ then ||u||=$\displaystyle \sqrt{x^2_1+x^2_2+...+x^2_n}$
cu=$\displaystyle (cx_1, cx_2,...,cx_n)$ then ||cu||=$\displaystyle \sqrt{(cx_1)^2+(cx_2)^2+...+(cx_n)^2}=\sqrt{c^2x_1 ^2+c^2x_2^2+...+c^2x_n^2}=\sqrt{c^{2n}(x^2_1+x^2_2 +...+x^2_n)}$
I guess I messed something up because this looks like I disproved it.

2. Originally Posted by Jskid
Show that if c is a scalar then ||cu||=|c|||u||

let u$\displaystyle =(x_1, x_2, ..., x_n)$ then ||u||=$\displaystyle \sqrt{x^2_1+x^2_2+...+x^2_n}$
cu=$\displaystyle (cx_1, cx_2,...,cx_n)$ then ||cu||=$\displaystyle \sqrt{(cx_1)^2+(cx_2)^2+...+(cx_n)^2}=\sqrt{c^2x_1 ^2+c^2x_2^2+...+c^2x_n^2}=\sqrt{c^{2n}(x^2_1+x^2_2 +...+x^2_n)}$
I guess I messed something up because this looks like I disproved it.
Where did the $\displaystyle n$ come from in the $\displaystyle c^{2n}$

If I factor $\displaystyle 4x+4y+4z$ I get $\displaystyle 4(x+y+z)$ not $\displaystyle 4^3(x+y+z)$

3. Originally Posted by Jskid
Show that if c is a scalar then ||cu||=|c|||u||

let u$\displaystyle =(x_1, x_2, ..., x_n)$ then ||u||=$\displaystyle \sqrt{x^2_1+x^2_2+...+x^2_n}$
cu=$\displaystyle (cx_1, cx_2,...,cx_n)$ then ||cu||=$\displaystyle \sqrt{(cx_1)^2+(cx_2)^2+...+(cx_n)^2}=\sqrt{c^2x_1 ^2+c^2x_2^2+...+c^2x_n^2}=\sqrt{c^{2n}(x^2_1+x^2_2 +...+x^2_n)}$
I guess I messed something up because this looks like I disproved it.
$\displaystyle \sqrt{c^{2}(x^2_1+x^2_2+...+x^2_n)}=\sqrt{c^2}\cdo t\sqrt{(x^2_1+x^2_2+...+x^2_n)}=\cdots$