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NDA 2019 Maths · Mathematics · Vector Algebra · easy

The vector hat i+hat j+√2 hat k makes an angle θ with the positive direction of the z-axis. Then θ equals

Single correct option

The vector i^+j^+2 k^\hat i+\hat j+\sqrt2\,\hat k makes an angle θ\theta with the positive direction of the z-axis. Then θ\theta equals
  1. A. 30∘30^\circ
  2. B. 60∘60^\circ
  3. C. 45∘45^\circ
  4. D. 90∘90^\circ
Show answer and solution

Answer: (C) 45∘45^\circ

The magnitude is 1+1+2=2\sqrt{1+1+2}=2, so the direction cosine with the z-axis is cos⁡θ=22=12\cos\theta=\frac{\sqrt2}{2}=\frac1{\sqrt2} and θ=45∘\theta=45^\circ. The angles with the x- and y-axes are 60∘60^\circ each, since their cosine is 12\frac12. The direction cosine uses the magnitude 22 and not the component alone.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake