If the vectors $2 \hat{i}-3 \hat{j}+6 \hat{k}$ and $\bar{b}$ are collinear and $|\bar{b}|=14$, then…

If the vectors $2 \hat{i}-3 \hat{j}+6 \hat{k}$ and $\bar{b}$ are collinear and $|\bar{b}|=14$, then $\bar{b}$ has the value
  1. $4 \hat{i}+6 \hat{j}+12 \hat{k}$
  2. $-4 \hat{i}-6 \hat{j}-12 \hat{k}$
  3. $4 \hat{i}-6 \hat{j}+12 \hat{k}$
  4. $12 \hat{i}+5 \hat{j}+\sqrt{17} \widehat{k}$

Solution

$\vec{b}=14\left(\frac{2 \hat{i}-3 \hat{j}+6 \hat{k}}{\sqrt{2^2+(-3)^2+6^2}}\right)=14\left(\frac{2 \hat{i}-3 \hat{j}+6 \hat{k}}{7}\right)=4 \hat{i}-6 \hat{j}+12 \hat{k}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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