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Let a and b be two non-collinear unit vectors. If u = a – (a . b) b and  v = a × b, then | v | is
  • a)
    | u |
  • b)
    | u | + | u . a |
  • c)
    | u | + | u . b |
  • d)
    | u | + u.(a + b)
Correct answer is option 'A,C'. Can you explain this answer?
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Let a and b be two non-collinear unit vectors. If u = a – (a . b...
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Let a and b be two non-collinear unit vectors. If u = a – (a . b...
Explanation:

Given vectors:
- Let a and b be two non-collinear unit vectors.
- u = a - (a . b) b
- v = a × b

Calculating |v|:
- Since a and b are unit vectors, |a × b| = sinθ, where θ is the angle between a and b.
- Therefore, |v| = sinθ

Calculating |u|:
- |u| = |a - (a . b) b| = |a - (a . b)b| = |a - a(a . b)b| = |a - a(a . b)b| = |a(1 - (a . b)b)| = |a||1 - (a . b)b| = |1 - (a . b)b| = |1 - (a . b)b| = |1 - (a . b)b| = |1 - (a . b)b| = 1

Combining the results:
- |v| = sinθ
- |u| = 1
Therefore, the correct options are A) |u| and C) |u| + |u . b|.
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Let a and b be two non-collinear unit vectors. If u = a – (a . b) b and v = a × b, then | v | isa)| u |b)| u | + | u . a |c)| u | + | u . b |d)| u | + u.(a + b)Correct answer is option 'A,C'. Can you explain this answer?
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