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Three-dimensional space

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4. What are the projections of the point (2, 3, 5) on the xy, yz-, and xz-planes? Draw a rectangular box with the origin and (2, 3, 5) as opposite vertices and with its face parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagonal of the box.

8. Find the lengths of the sides of the triangle with vertices A(1, 2, -3), B(3, 4, -2), and C(3, -2,1). Is ABC a right triangle? Is it an isosceles triangle?

11. Find an equation of the sphere with center (1, -4, 3) and radius 5. What is the intersection of the sphere with the xz-plane?

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Topics in this set include three-dimensional space: finding equation of a sphere, lengths of sides of a triangle, and projections.

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