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TS EAMCET · Maths · Straight Lines

If \(12 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}-18 \hat{\mathbf{k}},-3 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-9 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-24 \hat{\mathbf{k}}\) be the position vectors of the vertices \(A, B\) and \(C\) respectively of \(\triangle A B C\), then the position vector of the incentre of \(\triangle A B C\) is

  1. A \(12 \hat{i}-15 \hat{j}-51 \hat{k}\)
  2. B \(6 \hat{i}-\frac{15}{2} \hat{j}-\frac{51}{2} \hat{k}\)
  3. C \(\frac{4}{3} \hat{i}-\frac{5}{3} \hat{j}-17 \hat{k}\)
  4. D \(4 \hat{i}-5 \hat{j}-17 \hat{k}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4 \hat{i}-5 \hat{j}-17 \hat{k}\)

Step-by-step Solution

Detailed explanation

We have, \(\mathbf{O A}=12 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}-18 \hat{\mathbf{k}}\) \(\mathbf{O B}=-3 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-9 \hat{\mathbf{k}}\) and \(\quad \mathbf{O C}=3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-24 \hat{\mathbf{k}}\)…