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AP EAMCET · Maths · Vector Algebra

Let \(\bar{a}=4 \bar{i}+3 \bar{j}\) and \(\bar{b}\) be two perpendicular vectors in the XOY-plane. A vector \(\bar{c}\) in the same plane and having projections 1 and 2 respectively on \(\bar{a}\) and \(\bar{b}\) is

  1. A \(\overline{\mathrm{i}}+2 \overline{\mathrm{j}}\)
  2. B \(2 \overline{\mathrm{i}}+\overline{\mathrm{j}}\)
  3. C \(\overline{\mathrm{i}}-2 \overline{\mathrm{j}}\)
  4. D \(2 \overline{\mathrm{i}}-\overline{\mathrm{j}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \overline{\mathrm{i}}-\overline{\mathrm{j}}\)

Step-by-step Solution

Detailed explanation

\(|\bar{a}| = \sqrt{4^2+3^2} = 5\) \(\hat{a} = \frac{4\bar{i}+3\bar{j}}{5}\) Let \(\hat{b}\) be a unit vector perpendicular to \(\bar{a}\). We choose \(\hat{b} = \frac{3\bar{i}-4\bar{j}}{5}\).…