# [SOLVED]Find vector w in terms of i and j

#### karush

##### Well-known member
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

Staff member
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

##### Well-known member
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

##### Well-known member
MHB Math Helper
Re: find vector w in terms of i and j

Everything you have written is correct.

#### MarkFL

Staff member
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...

#### karush

##### Well-known member
Re: find vector w in terms of i and j

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