Assertion and reason: equations of a line

Exercise and reference answers

Questions

1. Reason

   b − a points from the first point to the second.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   r = a + λ(b − a) passes through both given points.

2. Reason

   Its numerators fix the point and its denominators fix the direction.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The Cartesian form needs a point and a direction.

3. Reason

   Direction cosines are unique up to sign.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Direction ratios must be unique for a line.

Explanation