3D Geometry
Distance between Skew Lines
Grade 12
Question:
<p>Consider a tetrahedron D—ABC with position vectors of its angular points as A(1, 1, 1); B(1, 2, 3); C(1, 1, 2) and centre of tetrahedron <span>\left(\frac{3}{2}, \frac{3}{4}, 2\right)</span>. Find the shortest distance between the skew lines AB and CD.</p>
<p>(a) <span>\frac{1}{2}</span></p>
<p>(b) <span>\frac{1}{3}</span></p>
<p>(c) <span>\frac{1}{4}</span></p>
<p>(d) <span>\frac{1}{5}</span></p>
Step-by-Step Solution
Key Concept: Distance between skew lines is calculated using the formula involving the scalar triple product divided by the magnitude of cross product of direction vectors.
Using the formula for distance between skew lines with direction vectors and position vectors, the shortest distance is \frac{1}{3} .
Correct Answer: b