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Q3.5: NCERT Physics - Part 1 MOTION IN A PLANE 3.5 Solution: Read each statement below carefully and state with reasons, if…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often mistakenly assume that any three vectors can sum to zero if their magnitudes satisfy the triangle inequality, ignoring the geometric constraint that vector addition forming a closed loop requires coplanarity. Remember that three non-coplanar vectors span a 3D volume and cannot form a closed triangle, thus their resultant can never be a null vector.
Read each statement below carefully and state with reasons, if it is true or false: (a) The magnitude of a vector is always a scalar, (b) each component of a vector is always a scalar, (c) the total path length is always equal to the magnitude of the displacement vector of a particle. (d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.
Step-by-Step Verified Solution
**Answer:** (a) True. (b) False. (c) False. (d) True. (e) True.
**Step-by-Step Explanation:**
(a) Magnitude is a number, hence a scalar. [citation:1][citation:2]
(b) Each component of a vector is a scalar quantity (projection along an axis). [citation:2]
(c) Total path length is a scalar and is generally greater than or equal to displacement magnitude. [citation:1]
(d) Average speed � magnitude of average velocity because path length � displacement magnitude. [citation:2]
(e) Three non-coplanar vectors cannot form a closed triangle, so their sum cannot be zero. [citation:1][citation:2]
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