Browse Questions

# If $\overrightarrow a$ is any vector such that $\overrightarrow a\times \hat i+2\overrightarrow a-5\hat k=\overrightarrow 0$, then $\overrightarrow a=?$

Let $\overrightarrow a=x\hat i+y\hat j+z\hat k$,
Then $\overrightarrow a\times\hat i=z\hat j-y\hat k$
$\overrightarrow a\times\hat i+2\overrightarrow a-5\hat j=\overrightarrow 0$ $\Rightarrow\:$
$2x\hat i+(2y-5+z)\hat j+(2z-y)\hat j=0$
$\Rightarrow\:x=0,\:2y-5+z=0\:and\:2z-y=0$
$\Rightarrow\:z=1,\:y=2\:and\:x=0$
$\therefore\:\overrightarrow a=2\hat j+\hat k$