Let a be the position vector of a given point (x1, y1, z1), and r the position vector of any point (x, y, z). Describe the locus of r if (a) I r - a I = 3, (b) (r-a). a = 0, (c) (r-a).r = 0.

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Vikas TU · Answer

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Aditya Gupta · Answer

(a) | r - a | = 3 is a sphere with centre (x1, y1, z1) and radius 3. (b) (r-a). a = 0 is a plane passing through (x1, y1, z1) with normal a . (c) (r-a).r = 0 is a sphere with centre (x1/2, y1/2, z1/2) and radius | a| /2.

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Let a be the position vector of a given point (x1, y1, z1), and r the position vector of any point (x, y, z). Describe the locus of r if (a) I r - a I = 3, (b) (r-a). a = 0, (c) (r-a).r = 0.

Let a be the position vector of a given point (x1, y1, z1), and r the position vector of any point (x, y, z). Describe the locus of r if (a) I r - a I = 3, (b) (r-a). a = 0, (c) (r-a).r = 0.

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Let a be the position vector of a given point (x1, y1, z1), and r the position vector of any point (x, y, z). Describe the locus of r if (a) I r - a I = 3, (b) (r-a). a = 0, (c) (r-a).r = 0.

Let a be the position vector of a given point (x1, y1, z1), and r the position vector of any point (x, y, z). Describe the locus of r if (a) I r - a I = 3, (b) (r-a). a = 0, (c) (r-a).r = 0.

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