Find vector w in terms of i and j

[karush]

The vectors $\vec{i}$ , $\vec{j}$ are unit vectors
along the x-axis and y-axis respectively.

The vectors $ \vec{u}= –\vec{i} +2\vec{j}$ and $\vec{v} = 3\vec{i} + 5 \vec{j}$ are given.

(a) Find $\vec{u}+ 2\vec{v}$ in terms of $\vec{i}$ and $\vec{j}$ .

$–\vec{i} +2\vec{j} + 2(3\vec{i} + 5 \vec{j}) = 5\vec{i}+12\vec{j}$

A vector $\vec{w}$ has the same direction as $\vec{u} + 2\vec{v} $, and has a magnitude of $26$.

magnitude of $5\vec(i)+12\vec{j}$ is $\sqrt{5^2+12^2}=13$ which is half of $26$

(b) Find $\vec{w}$ in terms of $\vec{i}$and $\vec{j}$ .

so $\vec{w} = 2(5\vec{i}+12\vec{j}) = 10\vec{i}+24{j}$

hope so anyway??

 

[MarkFL]

Re: find vector w in terms of i and j

Your work is correct if \(\displaystyle \vec{v}\) is instead given as:

\(\displaystyle \vec{v}=2\vec{i}+5\vec{j}\)

Otherwise, the problem needs to be reworked.

 

[karush]

Re: find vector w in terms of i and j

Your work is correct if \(\displaystyle \vec{v}\) is instead given as:

\(\displaystyle \vec{v}=2\vec{i}+5\vec{j}\)

Otherwise, the problem needs to be reworked.

this is what was given $\displaystyle \vec{v}=3\vec{i}+5\vec{j}$

$\vec{u}+2\vec{v}= –\vec{i}+2\vec{j}+2(3\vec{i}+5\vec{j}) =5\vec{i}+12\vec{j}$
$–\vec{i}+6\vec{i}+2\vec{j}+10\vec{j}=5\vec{i}+12 \vec{j} $

this is a leading \(\displaystyle (-1)\vec{i}\) which hard to see...

or did I miss something else...

 

[Prove It]

Re: find vector w in terms of i and j

Everything you have written is correct.

 

[MarkFL]

Re: find vector w in terms of i and j

this is what was given $\displaystyle \vec{v}=3\vec{i}+5\vec{j}$

$\vec{u}+2\vec{v}= –\vec{i}+2\vec{j}+2(3\vec{i}+5\vec{j}) =5\vec{i}+12\vec{j}$
$–\vec{i}+6\vec{i}+2\vec{j}+10\vec{j}=5\vec{i}+12 \vec{j} $

this is a leading \(\displaystyle (-1)\vec{i}\) which hard to see...

or did I miss something else...

My apologies...I somehow missed the leading negative there...(Blush)

 

[karush]

Re: find vector w in terms of i and j

No prob...you are a lot more accurate than I am