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AP EAMCET · Maths · Straight Lines

If \(4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}\) are respectively the position vectors of the vertices \(A, B, C\) of \(\triangle A B C\), then the position vector of the point where the bisector of angle \(A\) meet \(\mathbf{B C}\) is

  1. A \(2 \hat{\mathbf{i}}+\frac{13}{3} \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\)
  2. B \(2 \hat{\mathbf{i}}-\frac{13}{3} \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\)
  3. C \(2 \hat{\mathbf{i}}+13 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\)
  4. D \(2 \hat{\mathbf{i}}+\frac{13}{3} \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \hat{\mathbf{i}}+\frac{13}{3} \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\)

Step-by-step Solution

Detailed explanation

As we know bisector of angle \(A\) divides the \(B C\) in ratio \(c: b\). where \(c\) is length of side \(A B=\sqrt{4+16+16}=6\) and \(b\) is length of side \(A C=\sqrt{4+4+1}=3\) \(\therefore\) Position vector of the point where the bisector of angle \(A\) meet \(\mathbf{B C}\)…