Mathematics › Vectors › Algebra of Vectors
$\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}-2 \hat{j}+3 \hat{k}, \bar{c}=\hat{i}-2 \hat{j}+\hat{k}$,…
$\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}-2 \hat{j}+3 \hat{k}, \bar{c}=\hat{i}-2 \hat{j}+\hat{k}$, then $a$ vector of magnitude 6 units, which is parallel to the vector $2 \bar{a}-\bar{b}+3 c$, is
$2 \hat{i}-4 \hat{j}+4 \hat{k}$ $\hat{i}-\hat{j}+2 \hat{k}$ $4 \hat{i}+4 \hat{j}-2 \hat{k}$ $2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ Solution
$\begin{aligned}
& \overline{\mathrm{a}}-\overline{\mathrm{b}}+3 \overline{\mathrm{c}} \\
= & (2-4+3) \hat{\mathrm{i}}+(2+2-6) \hat{\mathrm{j}}+(2-3+3) \hat{\mathrm{k}} \\
= & \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}
\end{aligned}$
$\therefore \quad$ Required vector is the multiple of the above vector and has magnitude 6 units.
Option (A) satisfies this condition.
Asked in: MHT CET 2024 (10 May Shift 2)
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