A man starts at the origin O and walks a distance of 3 units in the north- ea...

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Question Id : 11646 | Context :NIMCET 2024

Question

A man starts at the origin O and walks a distance of 3 units in the north- east direction and then walks a distance of 4 units in the north-west direction to reach the point P. then

$\vec{OP}$ is equal to

🎥 Video solution / Text Solution of this question is given below:

A man starts at the origin $O$ , walks 3 units in the north-east direction, then 4 units in the north-west direction to reach point $P$ . Find the displacement vector $\vec{OP}$ .

? Solution:

North-East (45°): $\vec{A} = 3 \cdot \left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) = \left( \frac{3}{\sqrt{2}}, \frac{3}{\sqrt{2}} \right)$
North-West (135°): $\vec{B} = 4 \cdot \left( -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) = \left( -\frac{4}{\sqrt{2}}, \frac{4}{\sqrt{2}} \right)$
Total Displacement: $\vec{OP} = \vec{A} + \vec{B} = \left( \frac{-1}{\sqrt{2}}, \frac{7}{\sqrt{2}} \right)$

✅ Final Answer:

$\boxed{ \vec{OP} = \left( \frac{-1}{\sqrt{2}},\ \frac{7}{\sqrt{2}} \right) }$

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A man starts at the origin O O , walks 3 units in the north-east direction, then 4 units in the north-west direction to reach point P P . Find the displacement vector →OP \vec{OP} .

? Solution:

✅ Final Answer:

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A man starts at the origin $O$ , walks 3 units in the north-east direction, then 4 units in the north-west direction to reach point $P$ . Find the displacement vector $\vec{OP}$ .