Question

A force \( \mathbf{F} = 2\hat{i} + 3\hat{j} + 5\hat{k} \) acts on a particle moving in the direction of \( \mathbf{r} = 2\hat{i} + 3\hat{j} + \beta \hat{k} \). Find the value of \( \beta \) when the work done is zero.

• A. \( \beta = -2 \)
• B. \( \beta = -3 \)
• C. \( \beta = -4 \)
• D. \( \beta = -5 \)

Hint:

In vector problems, if the work done is zero, the vectors involved must be perpendicular, so their dot product will be zero.

Answer 1

The Correct Option is B

For the work done to be zero, the force and displacement vectors must be perpendicular. This means their dot product must be zero. Calculate the dot product of the force vector and the displacement vector, set it equal to zero, and solve for \( \beta \).