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NDA 1 2024 Maths, question 67

Topic: Vectors

Q67

If a vector of magnitude 2 units2\text{ units} makes an angle π3\frac{\pi}{3} with 2i^2\hat{i}, π4\frac{\pi}{4} with 3j^3\hat{j} and an acute angle θ\theta with 4k^4\hat{k}, then what are the components of the vector ?

  1. (a) (1,2,1)(1,\sqrt{2},1)Correct answer
  2. (b) (1,−2,1)(1,-\sqrt{2},1)
  3. (c) (1,−2,−1)(1,-\sqrt{2},-1)
  4. (d) (1,2,−1)(1,\sqrt{2},-1)

Solution.

Answer: (a) (1,2,1)(1,\sqrt{2},1)

  1. For a vector of magnitude 2, the given direction angles give x-component 2 cos 60° = 1 and y-component 2 cos 45° = √2.
  2. Its positive z-component is √(4 − 1 − 2) = 1.
  3. Hence the vector is i + √2j + k.