Assertion and reason

Exercise and reference answers

Questions

1. Reason

   Any triple proportional to the direction cosines qualifies.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   A line has infinitely many sets of direction ratios.

2. Reason

   They are the components of a unit vector along the line.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Direction cosines always satisfy l² + m² + n² = 1.

3. Reason

   Skew lines never intersect.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Two skew lines can be contained in a single plane.

4. Reason

   The convention is to report the acute angle between two lines.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The angle formula carries a modulus sign.

Explanation