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Q3.6: NCERT Physics - Part 1 MOTION IN A PLANE 3.6 Solution: Establish the following vector inequalities geometrically or…
Establish the following vector inequalities geometrically or otherwise: (a) |a+b| � |a| + |b| (b) |a+b| � ||a| _ |b|| (c) |a_b| � |a| + |b| (d) |a_b| � ||a| _ |b||. When does the equality sign above apply?
Step-by-Step Verified Solution
**Answer:** (a) Equality when vectors are parallel and in same direction. (b) Equality when vectors are antiparallel. (c) Equality when vectors are antiparallel. (d) Equality when vectors are parallel and in same direction.
**Step-by-Step Explanation:**
(a) Triangle inequality: |a+b| � |a| + |b|. Equality when a and b are parallel (same direction). [citation:3][citation:6]
(b) |a+b| � ||a| _ |b||. Equality when a and b are antiparallel. [citation:3]
(c) |a_b| � |a| + |b|. Equality when a and b are antiparallel.
(d) |a_b| � ||a| _ |b||. Equality when a and b are parallel (same direction).
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