Curve C lies in the x y -plane and satisfies R ⋅ ( 2 i ^ − 2 j ^ ) − ∣ R ∣ 2 = 1 . Find the minimum distance from L to the centre of C .

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Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Given $a = \hat{i} + 2 \hat{j} - 3 \hat{k}, b = 2 \hat{i} - \hat{j} + \hat{k}$ , and line $L$ defined by $r \times b = a \times b$ .

Curve $C$ lies in the $x y$ -plane and satisfies $R \cdot (2 \hat{i} - 2 \hat{j}) - ∣ R ∣^{2} = 1$ . Find the minimum distance from $L$ to the centre of $C$ .

Options:

Answer:

Solution:

The curve is $x^{2} + y^{2} - 2 x + 2 y + 1 = 0$ , with centre (1, -1, 0). Its distance from $L$ is $23$ .

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Line ( Equation etc.)

⏱ 2mℹ️ Source: QB

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