First slide

Vectors

Question

Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneosuly $\vec{F_{1}} = - 4 \hat{i} - 5 \hat{j} + 5 \hat{k}$ , $\vec{F_{2}} = 5 \hat{i} + 8 \hat{j} + 6 \hat{k}$ , $\vec{F_{3}} = - 3 \hat{i} + 4 \hat{j} - 7 \hat{k}$ and $\vec{F_{4}} = 2 \hat{i} - 3 \hat{j} - 2 \hat{k}$ then the particle will move

Moderate

A

In x-y plane
B

In y-z plane
C

In x-z plane
D

Along x-axis

Solution

$\vec{F_{1}} + \vec{F_{2}} + \vec{F_{3}} + \vec{F_{4}} =$ $(- 4 \hat{i} + 5 \hat{i} - 3 \hat{i} + 2 \hat{i}) + (- 5 \hat{j} + 8 \hat{j} + 4 \hat{j} - 3 \hat{j}) + (5 \hat{k} + 6 \hat{k} - 7 \hat{k} - 2 \hat{k})$ $= 4 \hat{j} + 2 \hat{k}$
$∴$ the particle will move in y-z plane.

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