(B) Work done $(W)$ is defined as the dot product of force $(\vec{F})$ and displacement $(\vec{S})$: $W = \vec{F} \cdot \vec{S}$.Given $\vec{F} = 2\ha

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(B) Work done $(W)$ is defined as the dot product of force $(\vec{F})$ and displacement $(\vec{S})$: $W = \vec{F} \cdot \vec{S}$.Given $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ and $\vec{S} = \hat{i} - 2\hat{j} - \hat{k}$.Since the work done is zero,$W = (2\hat{i} + b\hat{j} + \hat{k}) \cdot (\hat{i} - 2\hat{j} - \hat{k}) = 0$.Calculating the dot product: $(2)(1) + (b)(-2) + (1)(-1) = 0$.$2 - 2b - 1 = 0$.$1 - 2b = 0$.$2b = 1$.Therefore,$b = \frac{1}{2}$.

Class 11 Physics Work, Energy, Power and Collision Work Done by Constant Force

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$A$ force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\vec{S} = \hat{i} - 2\hat{j} - \hat{k}$. What will be the value of $b$,if the work done on the particle is zero?

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A
$0$
B
$\frac{1}{2}$
C
$\frac{1}{3}$
D
$2$

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Work, Energy, Power and Collision

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Work Done by Constant Force

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$A$ force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\vec{S} = \hat{i} - 2\hat{j} - \hat{k}$. What will be the value of $b$,if the work done on the particle is zero?

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