The figure shows the orientation of two vectors u and v in the XY plane.

$\text{ If }\mathrm{u}=\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}\text{ and }\mathrm{v}=\mathrm{p}\hat{\mathrm{i}}+\mathrm{q}\hat{\mathrm{j}}$

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.

The component of a vector r along the X-axis will have maximum value if:

1. r is along the positive Y-axis

2. r is along the positive X-axis

3. r makes an angle of 45^o with the X-axis

4. r is along the negative Y-axis

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

Three vectors A, B, and C add up to zero. Then:
(a) vector (A×B)×C is not zero unless vectors B and C are parallel.
(b) vector (A×B).C is not zero unless vectors B and C are parallel.
(c) if vectors A, B and C define a plane, (A×B)×C is in that plane.
(d) (A×B).C = |A||B||C| $\to$ C² = A² + B²

The incorrect statement/s is/are:

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

It is found that |A + B| = |A|. This necessarily implies:

1. B = 0

2. A, B are antiparallel

3. A and B are perpendicular

4. A.B ≤ 0

If |A| = 2 and |B| = 4, then match the relations in column I with the angle θ between A and B in column II.

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)

For two vectors A and B, |A+B|=|A - B| is always true when:

(a) |A| = |B| $\ne$ 0

(b) $\mathrm{A} \perp \mathrm{B}$

(c) |A| = |B| $\ne$ 0 and A and B are parallel or antiparallel.

(d) when either |A| or |B| is zero.

Choose the correct option/s:

1. (a, d)

2. (b, c)

3. (b, d)

4. (a, b)

The angle between $\mathrm{A}=\hat{\mathrm{i}}+\hat{\mathrm{j}} \mathrm{and} \mathrm{B}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ is

1. 45° 

2. 90° 

3. –45° 

4. 180°