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MHT CET · Maths · Vector Algebra

In a triangle ABC with usual notations if \(|\overline{\mathrm{BC}}|=8,|\overline{\mathrm{CA}}|=7,|\overline{\mathrm{AB}}|=10\) then the projection of \(\overline{\mathrm{AB}}\) on \(\overline{\mathrm{AC}}\) is

  1. A \(\frac{14}{85}\) units
  2. B \(\frac{1}{85}\) units
  3. C \(\frac{85}{14}\) units
  4. D \(\frac{7}{85}\) units
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{85}{14}\) units

Step-by-step Solution

Detailed explanation

\( \cos A = \frac{|\overline{\mathrm{CA}}|^2 + |\overline{\mathrm{AB}}|^2 - |\overline{\mathrm{BC}}|^2}{2|\overline{\mathrm{CA}}||\overline{\mathrm{AB}}|} \) \( \cos A = \frac{7^2 + 10^2 - 8^2}{2 \cdot 7 \cdot 10} = \frac{49 + 100 - 64}{140} = \frac{85}{140} = \frac{17}{28} \)