A particle is displaced through $(3\hat i+4\hat j) ext{ m}$ by force $2\hat i ext{ N}$. The work done is:

Question

A particle is displaced through $(3\hat i+4\hat j)	ext{ m}$ by force $2\hat i	ext{ N}$. The work done is:

Accepted Answer

1. **Identify the Formula:** Work done ($W$) by a constant force is defined as the scalar (dot) product of the force vector ($\mathbf{F}$) and the displacement vector ($\mathbf{d}$).
   $$ W = \mathbf{F} \cdot \mathbf{d} $$ [Class 11 Physics, Ch 6, Sec 6.3, Eq 6.4]
2. **Identify Given Values:**
   $$ \mathbf{F} = 2\hat i	ext{ N} $$
   $$ \mathbf{d} = (3\hat i + 4\hat j)	ext{ m} $$
3. **Calculate Dot Product:**
   Using the property of scalar products of unit vectors where $\hat i \cdot \hat i = 1$ and $\hat i \cdot \hat j = 0$ [Class 11 Physics, Ch 6, Sec 6.1.1, Eq 5.1c]:
   $$ W = (2\hat i) \cdot (3\hat i + 4\hat j) $$
   $$ W = (2)(3)(\hat i \cdot \hat i) + (2)(4)(\hat i \cdot \hat j) $$
   $$ W = 6(1) + 8(0) = 6	ext{ J} $$

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