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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Vector Algebra

NDA 2023 · Mathematics · Vector Algebra

The vectors 60 i +3 j , 40 i -8 j \ and β i -52 j are collinear if:

The vectors 60i^+3j^,40i^−8j^  and βi^−52j^60 \hat{i}+3 \hat{j}, \quad 40 \hat{i}-8 \hat{j} \ \text{ and } \beta \hat{i}-52 \hat{j} are collinear if:

Options

  1. Aβ=20\beta=20
  2. Bβ=40\beta=40
  3. Cβ=−40\beta=-40
  4. Dβ=26\beta=26

Correct answer

C. β=−40\beta=-40

Step-by-step solution

For collinear of givenvectorsgiven vectors−8−340−60=−52+8β−40⇒−11−20=−44β−40⇒β−40=−80⇒β=−40\begin{aligned} & \frac{-8-3}{40-60}=\frac{-52+8}{\beta-40} \\ & \Rightarrow \frac{-11}{-20}=\frac{-44}{\beta-40} \\ & \Rightarrow \beta-40=-80 \\ & \Rightarrow \beta=-40 \end{aligned}$$
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