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Q3.7: NCERT Physics - Part 1 MOTION IN A PLANE 3.7 Solution: Given a + b + c + d = 0, which of the following statements are…
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Even when $a+b+c+d=0$, the individual vectors need not be zero; they can be non‑zero and cancel each other. Only the total sum vanishes, not each term.
Given a + b + c + d = 0, which of the following statements are correct: (a) a, b, c, and d must each be a null vector, (b) The magnitude of (a + c) equals the magnitude of (b + d), (c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d, (d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?
Step-by-Step Verified Solution
**Answer:** (b), (c), and (d) are correct.
**Step-by-Step Explanation:**
(a) Incorrect. It is not necessary for all vectors to be null.
(b) Correct. a + c = _(b + d), so |a + c| = |b + d|. [citation:2][citation:19]
(c) Correct. a = _(b + c + d), so |a| � |b| + |c| + |d| by triangle inequality. [citation:2]
(d) Correct. The vector (b + c) must lie in the plane of a and d for the sum to be zero. [citation:2][citation:19]
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