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#### karush

##### Well-known member

- Jan 31, 2012

- 2,779

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??