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Three Dimensional Geometry

Question

The plane x + 2y – z = 4 cuts the sphere x² + y² + z² – x + z – 2 = 0 in a circle of radius

3

1

2

$square root of 2$

Solution

Perpendicular distance of centre $open parentheses 1 half comma 0 comma fraction numerator negative 1 over denominator 2 end fraction close parentheses$ from x + 2y – 2 = 4
$fraction numerator open vertical bar begin display style 1 half plus 1 half minus 4 end style close vertical bar over denominator square root of 6 end fraction space equals space square root of 3 over 2 end root space radius space equals space square root of 5 over 2 minus 3 over 2 end root space equals space 1$

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Three Dimensional Geometry

The plane x + 2y – z = 4 cuts the sphere x² + y² + z² – x + z – 2 = 0 in a circle of radius

3

1

2

$square root of 2$

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius 3 1 2

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The plane x + 2y – z = 4 cuts the sphere x² + y² + z² – x + z – 2 = 0 in a circle of radius

3

1

2

$square root of 2$

If α, β, γ are the angles which a line makes with the axes, prove that sin²α + sin² β + sin²γ = 2.