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NDA 2020 Maths · Mathematics · Vector Algebra · medium

If the vectors 2hat i-3hat j+6hat k and μhat i+6hat j-12hat k are parallel, then μ is

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If the vectors 2i^−3j^+6k^2\hat i-3\hat j+6\hat k and μi^+6j^−12k^\mu\hat i+6\hat j-12\hat k are parallel, then μ\mu is
  1. A. −4-4
  2. B. 44
  3. C. −2-2
  4. D. 22
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Answer: (A) −4-4

Parallel vectors have proportional components: μ2=6−3=−126=−2\dfrac{\mu}{2}=\dfrac{6}{-3}=\dfrac{-12}{6}=-2. Hence μ=−4\mu=-4. Both component ratios 6−3\dfrac6{-3} and −126\dfrac{-12}{6} equal −2-2, confirming parallelism. The value −2-2 is the common ratio and not μ\mu, and 44 results from dropping the negative sign. Always multiply the ratio by the first component of the first vector.
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Original question written in the NDA 2020 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