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UPCET / UPSEE Incentre — practice questions

Explore 1 free Incentre questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Incentre questions and exercises with answers

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If $A(0, 3, 0), B(0, 0, 4), C(0, 3, 4)$ are vertices of a triangle, the position vector of its **incentre** is:Read the answer and worked solution →

Worked practice questions

If $A(0, 3, 0), B(0, 0, 4), C(0, 3, 4)$ are vertices of a triangle, the position vector of its **incentre** is:

  1. $2\hat j + 3\hat k$
  2. $3\hat j + 2\hat k$
  3. $\hat j + \hat k$
  4. $(\hat j + \hat k)/2$
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Correct answer: A. $2\hat j + 3\hat k$

**Compute side lengths:** $|AB| = 5, |AC| = 4, |BC| = 3$. Incentre $H = (|BC|\,\vec a + |AC|\,\vec b + |AB|\,\vec c)/(|BC|+|AC|+|AB|)$. **Substituting:** $H = (3(3\hat j) + 4(4\hat k) + 5(3\hat j + 4\hat k))/12 = (24\hat j + 36\hat k)/12 = 2\hat j + 3\hat k$, i.e. the point $(0, 2, 3)$.

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