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Three vectors \(A,B\) and \(C\) add up to zero. Then:
| 1. | vector \((A\times B)\times C\) is not zero unless vectors \(B\) and \(C\) are parallel. |
| 2. | vector \((A\times B).C\) is not zero unless vectors \(B\) and \(C\) are parallel. |
| 3. | if vectors \(A,B\) and \(C\) define a plane, \((A\times B)\times C\) is in that plane. |
| 4. | \((A\times B). C= |A||B||C|\rightarrow C^2= A^2+B^2\) |
The incorrect statement/s is/are:
1. (b), (d)
2. (a), (c)
3. (b), (c), (d)
4. (a), (b)
Subtopic: Â Vector Product |
Level 3: 35%-60%
Hints
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If \(\left| \vec{A}\right|\) = \(2\) and \(\left| \vec{B}\right|\) = \(4,\) 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) \(\left| \vec{A}\times \vec{B}\right|\) \(=0\) | (p) \(\theta=30^\circ\) |
| (B)\(\left| \vec{A}\times \vec{B}\right|\)\(=8\) | (q) \(\theta=45^\circ\) |
| (C) \(\left| \vec{A}\times \vec{B}\right|\) \(=4\) | (r) \(\theta=90^\circ\) |
| (D) \(\left| \vec{A}\times \vec{B}\right|\) \(=4\sqrt2\) | (s) \(\theta=0^\circ\) |
| 1. | A(s), B(r), C(q), D(p) |
| 2. | A(s), B(p), C(r), D(q) |
| 3. | A(s), B(p), C(q), D(r) |
| 4. | A(s), B(r), C(p), D(q) |
Subtopic: Â Vector Product |
 86%
Level 1: 80%+
Hints
- 1(current)
Q. No.
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