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AP EAMCET · Maths · Vector Algebra

If \(\mathrm{A}=(0,4,-3), \mathrm{B}=(5,0,12)\) and \(\mathrm{C}=(7,24,0)\), then \(\lfloor\mathrm{BAC}=\)

  1. A \(60^{\circ}\)
  2. B \(\operatorname{Cos}^{-1}\left(\frac{16}{\sqrt{13}}\right)\)
  3. C \(\operatorname{Cos}^{-1}\left(\frac{13}{38}\right)\)
  4. D \(90^{\circ}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(90^{\circ}\)

Step-by-step Solution

Detailed explanation

\(\vec{\mathrm{AB}} = \mathrm{B} - \mathrm{A} = (5-0, 0-4, 12-(-3)) = (5, -4, 15)\) \(\vec{\mathrm{AC}} = \mathrm{C} - \mathrm{A} = (7-0, 24-4, 0-(-3)) = (7, 20, 3)\) \(\vec{\mathrm{AB}} \cdot \vec{\mathrm{AC}} = (5)(7) + (-4)(20) + (15)(3) = 35 - 80 + 45 = 0\)…