Finding a component of a force given the resultant magnitude
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1. If the resultant of three forces $\vec{F}_1 = p\hat{i} + 3\hat{j} - \hat{k}$, $\vec{F}_2 = -5\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{F}_3 = 6\hat{i} - \hat{k}$ acting on a particle has magnitude equal to 5 units, then the value (s) of p is (are) (A) -6 (B) -4 (C) 2 (D) 4
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Hi Gnyanesh, let's solve this physics problem together. We are given three force vectors acting on a particle, and we know that the magnitude of their resultant is equal to five units. We need to find the possible values of the parameter p.
Given Force Vectors
The resultant force vector, which we will call F net, is the vector sum of these three individual forces.
Let us substitute the given expressions for each force vector into this equation.
Now, let's group the components along the i, j, and k unit vectors.
Simplifying the coefficients, we get p plus one along the i direction, four along the j direction, and zero along the k direction.
Now, let's find the magnitude of this resultant force. The magnitude of a vector is the square root of the sum of the squares of its components.
Magnitude of the Resultant Force
We are given that this magnitude is equal to five units, so we can equate this expression to five.
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