\(\overrightarrow {A}\) is a vector with magnitude \(A\), then the unit vector \(\hat{A}\) in the direction of \(\overrightarrow {A}\) is:
1. \(A\overrightarrow A\)
2. \(\overrightarrow A \cdot\overrightarrow A\)
3. \(\overrightarrow A \times \overrightarrow A\)
4. \(\frac{\overrightarrow A}{A}\)

If \(\overrightarrow {A}= 2\hat i + 4\hat j- 5\hat k,\) then the direction cosines of the vector are:

(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three \(+\)ve coordinate axes.)
1. \(\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}~\text{and}~\frac{-5}{\sqrt{45}}\)
2. \(\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{3}{\sqrt{45}}\)
3. \(\frac{4}{\sqrt{45}}, 0~\text{and}~\frac{4}{\sqrt{45}}\)
4. \(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{5}{\sqrt{45}}\)

The vector that must be added to the vector $\hat{\mathrm{i}}-3\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}}+6\hat{\mathrm{j}}-7\hat{\mathrm{k}}$ so that the resultant vector is a unit vecotr along the y-axis is

1. $4\hat{\mathrm{i}}+2\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

2. $-4\hat{\mathrm{i}}-2\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

3. $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

4. Null vector

Surface area is:

1. Scalar

2. Vector

3. Neither scalar nor vector

4. Both scalar and vector

A force \(F\) applied at a \(30^\circ\) angle to the \(x \)-axis has the following \(X\) and \(Y\) components:
1. \(\frac{F}{\sqrt{2}}, F\)
2. \(\frac{F}{2}, \frac{\sqrt{3}}{2}F\)
3. \(\frac{\sqrt{3}}{2}F, \frac{1}{2}F\)
4. \(F , \frac{F}{\sqrt{2}}\)

Angular momentum is

1. A scalar

2. A polar vector

3. An axial-vector

4. None of these

If \(\overrightarrow {P}= \overrightarrow {Q}\), then which of the following is NOT correct?
1. \(\widehat{P}= \widehat{Q}\)
2. \(\left|\overrightarrow {P}\right|= \left|\overrightarrow {Q}\right|\)
3. \(P\widehat{Q}= Q\widehat{P}\)
4. \(\overrightarrow {P}+ \overrightarrow {Q}= \widehat{P}+ \widehat{Q}\)

Which of the following is a scalar quantity

1. Displacement

2. Electric field

3. Acceleration

4. Work

There are two force vectors, one of \(5~\text{N}\) and the other of \(12~\text{N}\). At what angle should the two vectors be added to get the resultant vector of \(17~\text{N}, 7~\text{N},\) and \(13~\text{N}\) respectively:
1. \(0^{\circ}, 180^{\circ}~\text{and}~90^{\circ}\)
2. \(0^{\circ}, 90^{\circ}~\text{and}~180^{\circ}\)
3. \(0^{\circ}, 90^{\circ}~\text{and}~90^{\circ}\)
4. \(180^{\circ}, 0^{\circ}~\text{and}~90^{\circ}\)

If $\overrightarrow{\mathrm{A}}=4\hat{\mathrm{i}}-3\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$ then magnitude and direction of $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ will be

1. $5, {\tan }^{-1}(3/4)$

2. $5\sqrt{5}, {\tan }^{-1}(1/2)$

3. $10, {\tan }^{-1}\left(5\right)$

4. $25, {\tan }^{-1}(3/4)$