# 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 |
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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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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 |
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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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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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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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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%
From NCERT
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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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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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