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. | \(\vec{A}.\vec{B}\leq0\) |
If \(|\vec{A}|=2\) and \(|\vec{B}|=4\), then match the relations in column-I with the angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\) in column-II.
Column-I | Column-II | ||
(a) | \(\vec{A}.\vec{B}=0\) | (i) | \(\theta=0^{\circ}\) |
(b) | \(\vec{A}.\vec{B}=8\) | (ii) | \(\theta=90^{\circ}\) |
(c) | \(\vec{A}.\vec{B}=4\) | (iii) | \(\theta=180^{\circ}\) |
(d) | \(\vec{A}.\vec{B}=-8\) | (iv) | \(\theta=60^{\circ}\) |
Choose the correct answer from the options given below:
1. | (a)–(iii), (b)-(ii), (c)-(i), (d)-(iv) |
2. | (a)–(ii), (b)-(i), (c)-(iv), (d)-(iii) |
3. | (a)–(ii), (b)-(iv), (c)-(iii), (d)-(i) |
4. | (a)–(iii), (b)-(i), (c)-(ii), (d)-(iv) |