3D Geometry
Triangle in 3D Space
Grade 12
Question:
<p>The vertices of △ABC are A(2, 0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentre is S. P is a point equidistant from A, B, C and the origin O. The z-coordinate of H is:</p>
<p>(a) 1</p>
<p>(b) 1/2</p>
<p>(c) 1/6</p>
<p>(d) 1/3</p>
Step-by-Step Solution
Key Concept: The orthocentre is found as the intersection point of altitudes of the triangle. Use perpendicularity conditions to find the coordinates.
For orthocentre H of triangle ABC with vertices A(2, 0, 0), B(0, 1, 0), C(0, 0, 2), we use the property that H is the intersection of altitudes. The z-coordinate of H is 1/3.
Correct Answer: d