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AP EAMCET · Maths · Vector Algebra

Three vectors of magnitudes \(a, 2 a, 3 a\) are along the directions of the diagonals of 3 adjacent faces of a cube that meet in a point. Then, the magnitude of the sum of those diagonals is

  1. A \(4 a\)
  2. B \(5 a\)
  3. C \(6 a\)
  4. D \(8 a\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(5 a\)

Step-by-step Solution

Detailed explanation

Let the vectors of magnitude \(a, 2 a, 3 a\) are along \(O P, O Q, O R\), respectively. Then, vectors are \(O P, O Q, O R\) are \(a\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right), 2 a\left(\frac{\hat{j}+\hat{k}}{\sqrt{2}}\right), 3 a\left(\frac{\hat{k}+\hat{i}}{\sqrt{2}}\right)\)…