Question

a particle moves from point A(5,4,9) to point B(9,7,21).Find displacement vector​ and magnitude of displacement

Answer 1

Explanation:

the displacement vector is (4,3,12)

displacement= 13

Answer 2

Answer :

Given -

• A (5, 4, 9)
• B (9, 7, 21)
• A particle moves from point A to point B.

To Find -

• Displacement vector ?
• Magnitude of Displacement ?

Solution -

$\vec{OA} = 5\hat{i} + 4\hat{j} + 9\hat{k}$

$\vec{OB} = 9\hat{i} + 7\hat{j} + 21\hat{k}$

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

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

Hence,$\vec{AB} = (9\hat{i} + 7\hat{j} + 21\hat{k}) - (5\hat{i} + 4\hat{j} + 9\hat{k})$

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

So, The Final Answer is :

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

Now, Displacement = (4, 3, 12)

Squaring and adding : 4² + 3² + 12²

⇒ 16 + 9 + 144

⇒ 169

Finding its square root : √169 = 13 units.

Hence, Magnitude of Displacement = 13 units.