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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

Paragraph: Let a vector a =4 i -8 j +k make angles α, β, γ with the...

Paragraph: Let a vector a⃗=4i^−8j^+k\vec{a}=4 \hat{i}-8 \hat{j}+k make angles α,β,γ\alpha, \beta, \gamma with the positive directions of x,y,zx, y, z axes respectivelv,Question: What is cos⁡α\cos \alpha equal to?

Options

  1. A13\frac{1}{3}
  2. B49\frac{4}{9}
  3. C59\frac{5}{9}
  4. D23\frac{2}{3}

Correct answer

B. 49\frac{4}{9}

Step-by-step solution

a⃗=4i^−8j^+k^\vec{a}=4 \hat{i}-8 \hat{j}+\hat{k} If angle made with XX axis =αcos⁡α=l=a1a12+a22+a32⇒cos⁡α=442+(−8)2+(1)2⇒cos⁡α=49=\alpha\cos \alpha=l=\frac{a_1}{\sqrt{a_1^2+a_2^2+a_3^2}}\Rightarrow \quad \cos \alpha=\frac{4}{\sqrt{4^2+(-8)^2+(1)^2}}\Rightarrow \quad \cos \alpha=\frac{4}{9}
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