Question

A body is at rest under the action of three forces, two of which are f1=4icap, f2=-6j cap, the third force is

Answer 1

Solution:

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Answer 2

The third force is -4$\hat{i}$ + 6$\hat{j}$ + 0$\hat{k}$

Explanation:

When a body is in rest then the three forces acting on the body is in equilibrium.

When the forces are in equilibrium then the sum of the forces are equal to zero.

ΔF = 0

F₁ + F₂ + F₃ = 0

Where,

F₁ = 4$\hat{i}$ + 0$\hat{j}$ + 0$\hat{k}$

F₂ = 0$\hat{i}$ -6$\hat{j}$ + 0$\hat{k}$

On substituting the forces, we get,

(4$\hat{i}$ + 0$\hat{j}$ + 0$\hat{k}$) + (0$\hat{i}$ -6$\hat{j}$ + 0$\hat{k}$) + F₃ = 0

4$\hat{i}$ -6$\hat{j}$ + F₃ = 0

∴ F₃ = -4$\hat{i}$ + 6$\hat{j}$ + 0$\hat{k}$