Question

Will give medal and fan
Find the norm of the vector 2b-a
B=(4,-1) A=(2,7)
Please explain

Answer 1

2b = (8,-2)

c = 2b - a = (8,-2) - (2,7) = (6, -9)

||2b-a|| = ||c|| = sqrt((6)^2 + (-9)^2) = the norm

Answer 2

\(\large{\bbox[5pt, lightcyan ,border:2px solid #e65c00 ]{ \rm Example }}\)

Find \(\large\color{#e65c00}{ \displaystyle 2{\bf r}+3{\bf v} }\).

Given that: \(\large\color{#e65c00}{ \displaystyle {\bf r}=(3,8) =3{\bf i}+8{\bf j} }\)
\(\quad\large\color{#e65c00}{ \displaystyle {\bf v}=(5,4)=5{\bf i}+4{\bf j} }\)


\(\large{\bbox[5pt, lightcyan ,border:2px solid #e65c00 ]{ \rm Solution: }}\)

\(\large\color{#e65c00}{ \displaystyle {\bf r}=3{\bf i}+8{\bf j} \quad\Rightarrow \quad 2\cdot {\bf r}=2\cdot 3{\bf i}+2\cdot 8{\bf j} }\)
\(\large\color{#e65c00}{ \displaystyle \quad\Longrightarrow \quad 2{\bf r}=6{\bf i}+16{\bf j} }\)


\(\large\color{#e65c00}{ \displaystyle {\bf v}=5{\bf i}+4{\bf j} \quad\Rightarrow \quad 3\cdot {\bf r}=3\cdot5{\bf i}+3\cdot4{\bf j} }\)
\(\large\color{#e65c00}{ \displaystyle \quad\Longrightarrow \quad 3{\bf r}=15{\bf i}+12{\bf j} }\)


\(\large\color{#e65c00}{ \displaystyle 2{\bf r}+3{\bf v} =\left\{6{\bf i}+16{\bf j}\right\} +\left\{15{\bf i}+12{\bf j} \right\} }\)
\(\large\color{#e65c00}{ \displaystyle 2{\bf r}+3{\bf v} =\left\{6{\bf i}+15{\bf i}\right\} +\left\{12{\bf j}+16{\bf j} \right\} }\)
\(\large\color{#e65c00}{ \displaystyle \color{#009933}{2{\bf r}+3{\bf v}} =\color{#009933}{21{\bf i} +28{\bf j}} =\color{#009933}{\left(21,28\right)} }\)

Answer 3

Thx