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Problem The locus of a point equidistant from two given points whose position vectors are a \mathbf{a} a b \mathbf{b} b [ r − 1 2 ( a + b ) ] ⋅ ( a + b ) = 0 [ \mathbf{r} - \frac{1}{2}(\mathbf{a} + \mathbf{b}) ] \cdot (\mathbf{a} + \mathbf{b}) = 0 [ r − 2 1 ( a + b )] ⋅ ( a + b ) = 0 [ r − 1 2 ( a + b ) ] ⋅ ( a − b ) = 0 [ \mathbf{r} - \frac{1}{2}(\mathbf{a} + \mathbf{b}) ] \cdot (\mathbf{a} - \mathbf{b}) = 0 [ r − 2 1 ( a + b )] ⋅ ( a − b ) = 0 [ r − 1 2 ( a + b ) ] ⋅ a = 0 [ \mathbf{r} - \frac{1}{2}(\mathbf{a} + \mathbf{b}) ] \cdot \mathbf{a} = 0 [ r − 2 1 ( a + b )] ⋅ a = 0 [ r − ( a + b ) ] ⋅ b = 0 [\mathbf{r} - (\mathbf{a} + \mathbf{b})] \cdot \mathbf{b} = 0 [ r − ( a + b )] ⋅ b = 0 Browse the problem library