Question

A particle undergoes two Displacements represented vectorially as 2i^-3j^+5k^ and i^+3j^-4k^ what is net displacement? Find the magnitude of the net displacement?

Answer 1

Solution :-

• As total displacement vector is the sum of vectors of 2 individual displacements.

• After getting resultant displacement vector we can find the magnitude of it.

Total displacement = (2i^ - 3j^ + 5k^) + (i^ + 3j^ - 4k^)

⇒ (2i^ - 3j^ + 5k^) + (i^ + 3j^ - 4k^)

⇒ 2i^ - 3j^ + 5k^ + i^ + 3j^ - 4k^

⇒ 3i^ + k^

The magnitude of net displacement is :

$\bf{\rightarrow\:\:\sqrt{(3)^2+(1)^2} }$

$\bf{\rightarrow\:\:\sqrt{9+1} }$

$\bf{\rightarrow\:\:\sqrt{10} }$

Final Answer :-

The magnitude of net displacement is √10

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