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AP EAMCET · Maths · Vector Algebra

If \(\bar{a}=2 \bar{i}-3 \bar{j}+5 \bar{k}\) and \(\bar{b}=-\bar{i}+3 \bar{j}+3 \bar{k}\) are two vectors, then the vector of magnitude 28 units in the direction of the vector \(\bar{a}-\bar{b}\) is

  1. A \(3 \overline{\mathrm{i}}+6 \overline{\mathrm{j}}-2 \overline{\mathrm{k}}\)
  2. B \(12 \overline{\mathrm{i}}-24 \overline{\mathrm{j}}+8 \overline{\mathrm{k}}\)
  3. C \(3 \overline{\mathrm{i}}-6 \overline{\mathrm{j}}-2 \overline{\mathrm{k}}\)
  4. D \(12 \overline{\mathrm{i}}+24 \overline{\mathrm{j}}-8 \overline{\mathrm{k}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(12 \overline{\mathrm{i}}-24 \overline{\mathrm{j}}+8 \overline{\mathrm{k}}\)

Step-by-step Solution

Detailed explanation

\( \bar{a}-\bar{b} = (2-(-1))\bar{i} + (-3-3)\bar{j} + (5-3)\bar{k} = 3\bar{i}-6\bar{j}+2\bar{k} \) \( |\bar{a}-\bar{b}| = \sqrt{3^2+(-6)^2+2^2} = \sqrt{9+36+4} = \sqrt{49} = 7 \) \( \text{Unit vector} = \frac{3\bar{i}-6\bar{j}+2\bar{k}}{7} \)…