If the vectors a→=iˆ−jˆ+2kˆ,b→=2iˆ+4jˆ+kˆ and c→=λiˆ+jˆ+μkˆ are mutually orthogonal, then (λ,μ)=(2,−3)(−2,3)(3,−2)(−3,2)

Question

If the vectors a→=iˆ−jˆ+2kˆ,b→=2iˆ+4jˆ+kˆ and c→=λiˆ+jˆ+μkˆ are mutually orthogonal, then (λ,μ)=(2,−3)(−2,3)(3,−2)(−3,2)
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Solution 1

The vectors a, b, and c are mutually orthogonal if their dot products are zero. This means that:

a.b = 0 a.c = 0 b.c = 0

Let's calculate these dot products:

  1. a.b = (iˆ−jˆ+2kˆ).(2iˆ+4jˆ+kˆ) = 21 - 14 + 2*1 = 0
  2. a.c = (iˆ−jˆ+2kˆ).(λiˆ+jˆ+μkˆ) = λ1 - 11 + 2*μ = 0
  3. b.c = (2iˆ+4jˆ+kˆ).(λiˆ+j Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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