If the vectors $$2\hat{i}-3\hat{j}+6\hat{k}$$, $$\vec{b}$$ are collinear and $$|b|=14$$, then $$\vec{b}=$$
Given :
vectors $$2\hat{i}-3\hat{j}+6\hat{k}, \vec{b}$$ are collinear
$$\implies \vec{b}=k(2\hat{i}-3\hat{j}+6\hat{k})$$ (property of collinearity) ...... $$(1)$$
$$\implies |\vec{b}|=|k(2\hat{i}-3\hat{j}+6\hat{k})|$$
Putting $$\left | \vec{b} \right |=14$$ in equation $$(1)$$, we get
$$k\left | 2\hat{i}-3\hat{j}+6\hat{k} \right |=14$$
$$\implies k\times (7)=14$$
$$\implies k=2$$
Thus, $$\vec{b}=4\hat{i}-6\hat{j}+12\hat{k}$$
hence, option $$B$$ is correct.
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