Vector Algebra
Applications of Vector Algebra in Triangles
Grade 12
Question:
<p><strong>Example 29.</strong> The position vectors of the vertices A, B and C of a triangle are \(\vec{i} - \vec{j} - 3\vec{k}\), \(2\vec{i} + \vec{j} - 2\vec{k}\) and \(-5\vec{i} + 2\vec{j} - 6\vec{k}\), respectively. The length of the bisector AD of the \(\angle BAC\), where D is on the segment BC, is</p>
<p>(a) \(\sqrt{10}\)</p>
<p>(b) \(\frac{3}{4}\)</p>
<p>(c) \(\frac{11}{2}\)</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Use the angle bisector theorem: the angle bisector divides the opposite side in the ratio of the adjacent sides. Then apply the section formula to find point D and finally compute the distance AD.
Solution: The answer is (b).
Correct Answer: B