Two vector $\overrightarrow{A}=2\hat{i}+3\hat{j}-4\hat{k}\text{and}\overrightarrow{B}=4\hat{i}+8\hat{j}+x\hat{k}$ are such that the component of $\overrightarrow{B}\text{along}\overrightarrow{A}$  is zero. Then the value of x will be :

$\overline{B}=4\hat{i}+8\hat{j}+xk$

$\overrightarrow{B}\text{along}\overline{A}=\frac{\overline{A}\left(\overline{A}.\overline{B}\right)}{{\text{A}}^2}=0$

$\overline{A}\left(\overline{A}.\overline{B}\right)=0$

$\overline{A}.\overline{B}=0$

$\overline{A}.\overline{B}=\left(2\hat{i}+3\hat{j}-4\hat{k}\right).\left(4\hat{i}+8\hat{j}+xk\right)=0$

$=8+24-4x=0$

$=32-4x=0$

$32=4x$

$\frac{32}{4}=x$

$x=8$