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TS EAMCET · Maths · Vector Algebra

If the vectors \(\mathrm{AB}=-3 \mathbf{i}+4 \mathbf{k}\) and \(\mathrm{AC}=5 \mathbf{i}-2 \mathbf{j}+4 \mathbf{k}\) are the sides of a \(\triangle A B C\), then the length of the median through \(A\) is

  1. A \(\sqrt{14}\)
  2. B \(\sqrt{18}\)
  3. C \(\sqrt{25}\)
  4. D \(\sqrt{29}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{18}\)

Step-by-step Solution

Detailed explanation

\(\therefore\) Position vector of \(\mathrm{AD}\) \(\begin{aligned} & =\frac{1(-3 \mathbf{i}+4 \mathbf{k})+1(5 \mathbf{i}-2 \mathbf{j}+4 \mathbf{k})}{1+1} \\ & =\mathbf{i}-\mathbf{j}+4 \mathbf{k} \\ & \therefore|\mathrm{AD}|=\sqrt{1+1+16}=\sqrt{18}\end{aligned}\)