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) when either |\(\vec A\)| or |\(\vec B\)| is zero.

Choose the correct option:
1. (a), (d)
2. (b), (c)
3. (b), (d)
4. (a), (b)

Subtopic:  Resultant of Vectors |
 55%
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The angle between \(\mathrm{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(\mathrm{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) is:
1. \(45^{\circ} \)
2. \(90^{\circ} \)
3. \(-45^{\circ} \)
4. \(180^{\circ}\)
Subtopic:  Scalar Product |
 78%
From NCERT
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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:  Vector Product |
 87%
From NCERT
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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)
Subtopic:  Scalar Product |
 88%
From NCERT
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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)

Subtopic:  Resultant of Vectors |
 70%
From NCERT
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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. \(\vec{A}.\vec{B}\leq0\)

Subtopic:  Resultant of Vectors |
From NCERT
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Three vectors A, B, and C add up to zero. Then:

1. vector (A×B)×C is not zero unless vectors B and C are parallel.
2. vector (A×B).C is not zero unless vectors B and C are parallel.
3. if vectors A, B and C define a plane, (A×B)×C is in that plane.
4. (A×B).C = |A||B||C|  → C2 = A2 + B2


The incorrect statement/s is/are:

1. (b, d)
2. (a, c)
3. (b, c, d)
4. (a, b)

Subtopic:  Vector Product |
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Consider the quantities of pressure, power, energy, impulse, gravitational potential, electric charge, temperature, and area. Out of these, the only vector quantities are:

1. impulse, pressure, and area
2. impulse and area
3. area and gravitational potential
4. impulse and pressure

Subtopic:  Scalars & Vectors |
From NCERT
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The component of a vector \(\vec{r}\) along the X-axis will have maximum value if:

1. \(\vec{r}\) is along the positive Y-axis.
2. \(\vec{r}\) is along the positive X-axis.
3. \(\vec{r}\) makes an angle of \(45^\circ\) with the X-axis.
4. \(\vec{r}\) is along the negative Y-axis.

Subtopic:  Resolution of Vectors |
 68%
From NCERT
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The figure shows the orientation of two vectors \(u\) and \(v\) in the XY plane.
If \(u=a\hat{i}+b\hat{j}\) and \(v=p\hat{i}+q\hat{j}\).

      
Which of the following is correct?

1. \(a\) and \(p\) are positive while \(b\) and \(q\) are negative.
2. \(a,\) \(p\) and \(b\) are positive while \(q\) is negative.
3. \(a,\) \(q\) and \(b\) are positive while \(p\) is negative.
4.  \(a,\) \(b,\) \(p\) and \(q\) are all positive.

Subtopic:  Resolution of Vectors |
 63%
From NCERT
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