If $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}+3 \hat{j}+4 \hat{k}$ and $\bar{c}=\hat{i}+\alpha…
If $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}+3 \hat{j}+4 \hat{k}$ and $\bar{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k}$ are linearly dependent vectors and $|\overline{\mathrm{c}}|=\sqrt{3}$, then the values of $\alpha$ and $\beta$ are respectively.
1,1
2,1
0,1
1,2
Solution
Note that only for option (A), i.e., for $\alpha=1$ and $\beta=1,|\vec{c}|=\sqrt{3}$ holds true.
$\therefore \quad$ Option (A) is correct.