Para encontrarmos o valor de X, realizaremos os cálculos abaixo:

\(\begin{align} & v=\left( -1,-1,-2 \right) \\ & A=\text{ }\left( 0,3,4 \right) \\ & ~B=\left( x,\text{ }-1,2 \right) \\ & \\ & \cos \theta =\frac{v\cdot ab}{|v||ab|} \\ & \cos 30=\frac{(-1,-1,-2)(x,-4,-2)}{|\sqrt{{{1}^{2}}+{{1}^{2}}+4}||\sqrt{{{x}^{2}}+16+{{2}^{2}}}|} \\ & 0,86=\frac{-x+8}{|\sqrt{6}||\sqrt{{{x}^{2}}+20}|} \\ & 2,10=\frac{-x+8}{\sqrt{{{x}^{2}}+20}} \\ & {{\left( \sqrt{{{x}^{2}}+20} \right)}^{2}}={{\left( \frac{-x+8}{2,10} \right)}^{2}} \\ & {{x}^{2}}+20=\frac{{{x}^{2}}-16x+64}{4,41} \\ & 4,41{{x}^{2}}+88,2={{x}^{2}}-16x+64 \\ & 3,41{{x}^{2}}+16x+24,2=0 \\ & x=\mathbf{4},42 \\ \end{align}\ \)

Portanto temos que x=4,42.