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Assertion and reason: products

Exercise and reference answers

Questions
  1. Reason
    It is defined using cos θ, which can be isolated.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    The scalar product can find the angle between two vectors.
  2. Reason
    It is defined along a unit vector normal to their plane.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    a × b is perpendicular to both a and b.
  3. Reason
    The scalar product returns a number.
    Verdict
    Both are true; the reason does not explain the assertion.
    Assertion
    A vector can be scaled by a negative number.

Explanation

Both halves can be true without one explaining the other. Source: syllabus Maths Part II, Ch 10 Vector Algebra.
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