The angle subtended by the vector $\mathrm{A} = 4\stackrel{\wedge }{\mathrm{i}} + 3\stackrel{\wedge }{\mathrm{j}} + 12\stackrel{\wedge }{\mathrm{k}}$ with the x-axis

• ${\sin }^{-1}\left(\frac{3}{13}\right)$

• ${\sin }^{-1}\left(\frac{4}{13}\right)$

• ${\cos }^{-1}\left(\frac{4}{13}\right)$

• ${\cos }^{-1}\left(\frac{3}{13}\right)$

$\overrightarrow{\mathrm{A} }\mathrm{and} \overrightarrow{\mathrm{B}}$ are two vectors given by $\overrightarrow{\mathrm{A}} = 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}} = \hat{\mathrm{i}} + \hat{\mathrm{j}}$. The magnitude of the component of $\overrightarrow{\mathrm{A}}$along $\overrightarrow{\mathrm{B}}$ is 

• $\frac{5}{\sqrt{2}}$

• $\frac{3}{\sqrt{2}}$

• $\frac{7}{\sqrt{2}}$

• $\frac{1}{\sqrt{2}}$

Given $\overrightarrow{\mathrm{C}} = \overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}} \mathrm{and} \overrightarrow{\mathrm{D}} = \overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{A}}$. What is the angle between $\overrightarrow{\mathrm{C}} \mathrm{and} \overrightarrow{\mathrm{D}}$ ?

• 30°

• 60°

• 90°

• 180°

214.

A bullet is fired with a velocity u making an angle of 60° with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is

• u

• 0

• $\frac{\sqrt{3\mathrm{u}}}{2}$

• $\frac{\mathrm{u}}{2}$

A particle is projected at 60° to the horizontal with a kinetic energy KE. The kinetic energy at the highest point is

• KE

• zero

• $\frac{\mathrm{KE}}{4}$

• $\frac{\mathrm{KE}}{2}$

A body is projected with a speed u m/s at an angle β with the horizontal. The kinetic energy at the highest point is $\frac{3}{4}$th of the initial kinetic energy. The value of β is

• 30°

• 45°

• 60°

• 120°

A ball is projected horizontally with a velocity of 5 m/s from the top of a building 19.6 m high. How long will the ball take to hit the ground ?

• $\sqrt{2} \mathrm{s}$

• 2 s

• $\sqrt{3} \mathrm{s}$

• 3 s

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for

• 6 s

• 5 s

• 7 s

• 4 s

The value of λ for which the two vectors $\overrightarrow{\mathrm{a}} = 5 \hat{\mathrm{i}} + \mathrm{\lambda } \hat{\mathrm{j}} + \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}} = \hat{\mathrm{i}} - 2 \hat{\mathrm{j}} + \hat{\mathrm{k}}$ are perpendicular to each other is

• 2

• - 2

• 3

• - 3

If $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} = \overrightarrow{\mathrm{c}}$ and a + b = c, the the angle included between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is

• 90°

• 180°

• 120°

• zero