Question

$If \vec{O A} = 2 \vec{i} + 5 \vec{j} - 2 \vec{k} and \vec{O B} = 3 \vec{i} + 6 \vec{j} + 5 \vec{k} then \vec{A B} =$

$\vec{i} + \vec{j} + 7 \vec{k}$
$5 \vec{i} + 2 \vec{j} + \vec{k}$
$\vec{i} + 2 \vec{j} - 7 \vec{k}$
$\vec{i} - \vec{j} - \vec{k}$

Answer: $\vec{i} + \vec{j} + 7 \vec{k}$

Solution :-

Given that $\vec{O A} = 2 \vec{i} + 5 \vec{j} - 2 \vec{k} and \vec{O B} = 3 \vec{i} + 6 \vec{j} + 5 \vec{k}$ , then

\begin{aligned} \vec{A B} & = & \vec{O B} - \vec{O A} (Because, ∣ \vec{O B} ∣ > ∣ \vec{O A} ∣) \\ = & (3 \vec{i} + 6 \vec{j} + 5 \vec{k}) - (2 \vec{i} + 5 \vec{j} - 2 \vec{k}) \\ = & 3 \vec{i} + 6 \vec{j} + 5 \vec{k} - 2 \vec{i} - 5 \vec{j} + 2 \vec{k} \\ = & (3 - 2) \vec{i} + (6 - 5) \vec{j} + (5 + 2) \vec{k} \\ = & \vec{i} + \vec{j} + 7 \vec{k} \cdot \end{aligned}

So, correct answer is option-1, $\to \vec{i} + \vec{j} + 7 \vec{k}$

#Vector Algebra #BSEB PYQ 2017 #Mathematics #BSEB PYQs