Given below in Column-I are the relations between vectors \(a,\) \(b,\) and \(c\) and in Column-II are the orientations of \(a,\) \(b,\) and \(c\) in the \(xy\)-plane. Match the relation in Column-I to the correct orientations in Column-II.
Column-I | Column-II | ||
(a) | \(a + b = c\) | (i) | ![]() |
(b) | \(a- c = b\) | (ii) | ![]() |
(c) | \(b - a = c\) | (iii) | ![]() |
(d) | \(a + b + c = 0\) | (iv) | ![]() |
Choose the correct option from the given table.
1. | a-(ii), b-(iv), c-(iii), d-(i) |
2. | a-(i), b-(iii), c-(iv), d-(ii) |
3. | a-(iv), b-(iii), c-(i), d-(ii) |
4. | a-(iii), b-(iv), c-(i), d-(ii) |
For two vectors \(\vec A\) and \(\vec B\), |\(\vec A\)+\(\vec B\)|=|\(\vec A\) - \(\vec B\)| is always true when:
(a) | \(\vec A\)| = |\(\vec B\)| ≠ \(0\) | |
(b) | \(\vec A\perp\vec B\) |
(c) | |\(\vec A\)| = |\(\vec B\)| ≠ \(0\) and \(\vec A\) and \(\vec B\) are parallel or antiparallel. |
(d) | \(\vec A\)| or |\(\vec B\)| is zero. | when either |
1. | (a), (d) |
2. | (b), (c) |
3. | (b), (d) |
4. | (a), (b) |