Question

A particle moves from point A(4, 0, 3) to point B(1, 4.-9). The unit vector along its displacement (AB) will be:

Answer 1

Answer :

Given -

• A (4, 0, 3)
• B (1, 4, -9)
• A particle moves from point A to point B.

To Find -

• Displacement vector ?

Solution -

$\vec{OA} = 4\hat{i} + 0\hat{j} + 3\hat{k}$

$\vec{OB} = 1\hat{i} + 4\hat{j} - 9\hat{k}$

We know that, $\vec{Displacement} = \vec{OB} - \vec{OA}$

So, $\vec{AB} = \vec{OB} - \vec{OA}$

Hence,

$\vec{AB} = (1\hat{i} + 4\hat{j} - 9\hat{k}) - (4\hat{i} + 0\hat{j} + 3\hat{k})$

$\vec{AB} = -3\hat{i} + 4\hat{j} - 12\hat{k}$

So, The Final Answer is :

$\vec{Displacement} = \vec{AB} = -3\hat{i} + 4\hat{j} - 12\hat{k}$