Two vectors $\overrightarrow{\mathit{x}}$ and $\overrightarrow{\mathit{y}}$ are collinear if $\overrightarrow{\mathit{x}}$ = $\mathit{\lambda }\overrightarrow{\mathit{y}}$ , where λ is a constant
Now, the vectors $2\hat{\mathit{i}}-3\hat{\mathit{j}}+4\hat{\mathit{k}}$ and $\mathit{a}\hat{\mathit{i}}+6\hat{\mathit{j}}-8\hat{\mathit{k}}$ are collinear
∴ $2\hat{\mathit{i}}-3\hat{\mathit{j}}+4\hat{\mathit{k}}$ = λ . $\left(\mathit{a}\hat{\mathit{i}}+6\hat{\mathit{j}}-8\hat{\mathit{k}}\right)$ , where λ is a constant.
⇒ 2 = λ a , - 3 = 6 λ , 4 = - 8 λ
Now, - 3 = 6λ or 4 = - 8λ ⇒ λ = $-\frac{1}{2}$
2 = λa
⇒ 2 = $-\frac{1}{2}$ a
⇒ a = - 4