Assertion and reason

Exercise and reference answers

Questions

1. Reason

   Its initial and terminal points are the same, so no direction is picked out.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The zero vector has no definite direction.

2. Reason

   It is defined as |a||b| cos θ, a product of three numbers.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   a · b is a number, not a vector.

3. Reason

   The cross product uses sin θ.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   a × b lies in the plane of a and b.

4. Reason

   That scales the magnitude to exactly 1 without turning it.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Dividing a vector by its magnitude gives a unit vector.

Explanation