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प्रश्न
If the distance between the points P(a, 2, 1) and Q (1, −1, 1) is 5 units, find the value of a.
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उत्तर
PQ = 5
\[\Rightarrow \sqrt{\left( 1 - a \right)^2 + \left( - 1 - 2 \right)^2 + \left( 1 - 1 \right)^2} = 5\]
\[ \Rightarrow \left( 1 - a \right)^2 + \left( - 3 \right)^2 = 25\]
\[ \Rightarrow 1 - 2a + a^2 + 9 - 25 = 0\]
\[ \Rightarrow a^2 - 2a - 15 = 0\]
\[ \Rightarrow \left( a - 5 \right)\left( a + 3 \right) = 0\]
\[ \Rightarrow a = 5, - 3\]
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