hi every one im new member in this fourm ..and i need your help...
this is the question
Suppose , and .
Compute the following values
||2u-4v+w||=
how to compute this????
I assume that you are trying to find $\displaystyle |2\mathbf{u} - 4\mathbf{v} + \mathbf{w}|$.
$\displaystyle 2\mathbf{u} - 4\mathbf{v} + \mathbf{w} = 2(3\mathbf{i} + \mathbf{j} + 5\mathbf{k}) - 4(5\mathbf{i} - 3\mathbf{j} + 3\mathbf{k}) + (-4\mathbf{i} - 4\mathbf{j} - 3\mathbf{k})$
$\displaystyle = 6\mathbf{i} +2\mathbf{j} + 10\mathbf{k} - 20\mathbf{i} + 12\mathbf{j} - 12\mathbf{k} -4\mathbf{i} - 4\mathbf{j} - 3\mathbf{k}$
$\displaystyle = -18\mathbf{i} + 10\mathbf{j} - 5\mathbf{k}$.
So $\displaystyle |2\mathbf{u} - 4\mathbf{v} + \mathbf{w}| = \sqrt{(-18)^2 + 10^2 + (-5)^2}$
$\displaystyle = \sqrt{324 + 100 + 25}$
$\displaystyle = \sqrt{449}$