AP EAMCET · Maths · Vector Algebra
Equation of the perpendicular bisector of the line joining the points whose position vectors are \(\mathbf{a}\) and \(\mathbf{b}\) respectively is
- A \((2 \mathrm{r}-\mathrm{a}-\mathrm{b}) \cdot(\mathrm{a}-\mathrm{b})=0\)
- B \((2 \mathrm{r}-\mathrm{a}-\mathrm{b}) \cdot(\mathrm{a}+\mathrm{b})=0\)
- C \((2 \mathrm{r}+\mathrm{a}+\mathrm{b}) \cdot(\mathrm{a}-\mathrm{b})=0\)
- D \((2 \mathrm{r}-\mathrm{a}+\mathrm{b}) \cdot(\mathrm{a}+\mathrm{b})=0\)
Answer & Solution
Correct Answer
(A) \((2 \mathrm{r}-\mathrm{a}-\mathrm{b}) \cdot(\mathrm{a}-\mathrm{b})=0\)
Step-by-step Solution
Detailed explanation
The mid-point of line joining points whose position vectors are \(\mathbf{a}\) and \(\mathbf{b}\) is \(M\left(\frac{\mathbf{a}+\mathbf{b}}{2}\right)\) and the direction ratio vector of line joining of given points is \((\mathbf{a}-\mathbf{b})\). Let a variable point…
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