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Does this produce a number or a vector?

Exercise and reference answers

Items
  1. Item
    a · b
    Category
    A number (scalar)
  2. Item
    |a|
    Category
    A number (scalar)
  3. Item
    a₁b₁ + a₂b₂ + a₃b₃
    Category
    A number (scalar)
  4. Item
    a × b
    Category
    A vector
  5. Item
    a + b
    Category
    A vector
  6. Item
    λa
    Category
    A vector
Categories
  1. Item
    A number (scalar)
  2. Item
    A vector

Explanation

The scalar product returns a number the cross product returns a vector perpendicular to both. Getting this backwards is the most expensive mistake in the chapter. Source: syllabus Maths Part II, Ch 10 Vector Algebra.
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