N2014 P1 Q3

N2014 P1 Q3

Junior College 2
5 marks
  1. It is given that \(\mathbf a\times\mathbf b=\mathbf0\). What can you deduce about the vectors \(\mathbf a\) and \(\mathbf b\)?[2]
  2. Find a unit vector \(\mathbf n\) such that \(\mathbf n\times(\mathbf i+2\mathbf j-2\mathbf k)=\mathbf0\).[2]
  3. Find the cosine of the acute angle between the vector \(\mathbf i+2\mathbf j-2\mathbf k\) and the \(z\)-axis.[1]

Solution:

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Answer:(i) Parallel non-zero vectors, or at least one zero vector. (ii) \(\mathbf n=\pm\frac13(\mathbf i+2\mathbf j-2\mathbf k)\). (iii) \(\frac23\).

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