2e:["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":2}] 31:T4f29,

\begin{aligned} \frac{\alpha-2}{2} & =\frac{\beta-3}{1}=\frac{\gamma-5}{-3}=\frac{-2(2 \times 2+3-3 \times 5-6)}{2^2+1^2+(-3)^2} \\\\ \frac{\alpha-2}{2} & =\frac{\beta-3}{1}=\frac{\gamma-5}{-3}=2 \\\\ \frac{\alpha-2}{2} & =2, \frac{\beta-3}{1}=2, \frac{\gamma-5}{-3}=2 \\\\ \alpha & =6, \beta=5, \gamma=-1 \end{aligned}

2f:["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$31"}}] 32:T946,Hence,

\alpha+\beta+\gamma=6+5-1=10

30:["$","li","2",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":3}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$32"}}]]}]

More on 3d Geometry

More on 3d Geometry