It is found that \(|\vec{A}+\vec{B}|=|\vec{A}|\). This necessarily implies:
1. | \(\vec{B}=0\) |
2. | \(\vec{A},\) \(\vec{B}\) are antiparallel |
3. | \(\vec{A}\) and \(\vec{B}\) are perpendicular |
4. | \(\vec{A}.\vec{B}\leq0\) |
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) |
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 |