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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

If β is perpendicular to both α and γ where α = k and γ =2 i +3 j...

If β⃗\vec{\beta} is perpendicular to both α⃗\vec{\alpha} and γ⃗\vec{\gamma} where α⃗=k^\vec{\alpha}=\hat{k} and γ⃗=2i^+3j^+4k^\vec{\gamma}=2 \hat{i}+3 \hat{j}+4 \hat{k}, then what is β⃗\vec{\beta} equal to?

Options

  1. A3i^+2j^3 \hat{i}+2 \hat{j}
  2. B−3i^+2j^-3 \hat{i}+2 \hat{j}
  3. C2i^−3j^2 \hat{i}-3 \hat{j}
  4. D−2i^+3j^-2 \hat{i}+3 \hat{j}

Correct answer

B. −3i^+2j^-3 \hat{i}+2 \hat{j}

Step-by-step solution

\overrightarrow{\mathrm{B}}= \pm\left|i^j^k^001234\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 0 & 0 & 1 \\ 2 & 3 & 4\end{array}\right|\overrightarrow{\mathrm{B}}= \pm 1(3 \hat{i}-2 \hat{j})= \pm(3 \hat{i}-2 \hat{j})
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