Vector Algebra
Distance in 3D Space
Grade 12
Question:
<p>The distance of the point having position vector <span style='font-style:italic;'>2i + 6j + 3k</span> from the straight line passing through the point <span style='font-style:italic;'>(2, 3, 4)</span> and parallel to the vector <span style='font-style:italic;'>i + 4j - 6k</span> is</p>
<p>(a) <span style='font-style:italic;'>2√13</span></p>
<p>(b) <span style='font-style:italic;'>4√3</span></p>
<p>(c) 6</p>
<p>(d) 7</p>
Step-by-Step Solution
Key Concept: Use the cross product formula to find the perpendicular distance from a point to a line in 3D space.
Note: This problem requires using the formula for distance from a point to a line in 3D space. The distance from point P to a line passing through point A with direction vector b is given by |(AP × b)| / |b| .
Correct Answer: a