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)

The vector sum of two forces is perpendicular to their vector difference. In that case, the forces:

1. are not equal to each other in magnitude.

2. cannot be predicted.

3. are equal to each other.

4. are equal to each other in magnitude.

If the angle between the two forces increases, the magnitude of their resultant:

1. Decreases

2. Increases

3. Remains unchanged

4. First decreases, then increases

If $∆ABC$ is right-angled at C, then the value of cos (A + B) is

1.  0

2.  1

3.  $\frac{1}{2}$

4.  $\frac{\sqrt{3}}{2}$

Which of the following is not possible?
1. sin θ = \(3\over5\)
2. sec θ = 100
3. cosec θ = 0.14
4. None of the above

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 the maximum value if-

1. r is oriented along the positive Y-axis

2. 3r is oriented 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

If the sum of two unit vectors is also a unit vector, then the magnitude of their difference and angle between the two given unit vectors is

1. $\sqrt{3}, 60°$

2. $\sqrt{3}, 120°$

3. $\sqrt{2}, 60°$

4. $\sqrt{2}, 120°$

Let $\mathrm{\theta }$ be the angle between vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$. Which of the following figures correctly represents the angle $\mathrm{\theta }$?
1. 

2. 

3.  

4. 

The dot product of two mutual perpendicular vector is:

1. 0

2. 1

3. $\infty$

4. None of the above