Question

Find u and v if 2u+4v=12i-18j-14k and 3u-2v=-14i+21j-13k.

Answer 1

Step-by-step explanation:

this is the answer you need

Answer 2

Answer:

Step-by-step explanation:

We have,

$\tt{2\vec{u}+4\vec{v}=12\hat{i}-18\hat{j}-14\hat{k}}\\\tt{3\vec{u}-2\vec{v}=-14\hat{i}+21\hat{j}-13\hat{k}}$

$\implies\tt{\vec{u}+2\vec{v}=6\hat{i}-9\hat{j}-7\hat{k}}\\\tt{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\vec{u}-2\vec{v}=-14\hat{i}+21\hat{j}-13\hat{k}}$

Add the above expressions

$\implies\tt{4\vec{u}=-8\hat{i}+12\hat{j}-20\hat{k}}$

$\implies\tt{\vec{u}=-2\hat{i}+6\hat{j}-5\hat{k}}$

Now,

$\tt{\vec{u}+2\vec{v}=6\hat{i}-9\hat{j}-7\hat{k}}$

$\tt{\implies2\vec{v}=6\hat{i}-9\hat{j}-7\hat{k}-\vec{u}}$

$\tt{\implies2\vec{v}=6\hat{i}-9\hat{j}-7\hat{k}-(-2\hat{i}+6\hat{j}-5\hat{k})}$

$\tt{\implies2\vec{v}=6\hat{i}-9\hat{j}-7\hat{k}+2\hat{i}-6\hat{j}+5\hat{k}}$

$\tt{\implies2\vec{v}=8\hat{i}-15\hat{j}-2\hat{k}}$

$\tt{\implies\vec{v}=4\hat{i}-\dfrac{15}{2}\hat{j}-\hat{k}}$