Two point masses 1 and 2 move with uniform velocities v → 1 and v → 2 , respectively. Their initial position vectors are r → 1 and r → 2 , respectively. Which of the following should be satisfied for the collision of the point masses?

r → 1 - r → 2 r → 2 - r → 2 = v → 2 - v → 1 v 2 → - v 1 →

r → 2 - r → 1 r 2 → - r q → = v → 2 - v → 1 v 2 → - v → 1

r → 2 - r → 1 r → 2 + r 1 → = v 2 → - v → 1 v → 2 + v 1 →

r → 2 + r → 1 r 2 → + r → 1 = v → 2 - v → 1 v 2 → + v 1 →

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The resultant of three vectors $1$ , $2$ and $3$ units whose directions are those of the sides of an equilateral triangle is at an angle of,

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Important Questions on Vectors

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IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 49

A unit vector along the incident ray of light is

\hat{i}

. The unit vector for the corresponding refracted ray of light is

\hat{r} . \hat{n}

, a unit vector normal to the boundary of the medium and directed towards the incident medium. If

μ

is the refractive index of the medium, then Snell’s law (second law) of refraction is,

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 50

The components of a vector along the

x

- and

y

-directions are

(n + 1)

and

1

, respectively. If the coordinate system is rotated by

θ = 60 °

, then the components change to

n

and

3

. The value of

n

is,

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 51

Two point masses

1

and

2

move with uniform velocities

{\vec{v}}_{1}

and

{\vec{v}}_{2}

, respectively. Their initial position vectors are

{\vec{r}}_{1}

and

{\vec{r}}_{2}

, respectively. Which of the following should be satisfied for the collision of the point masses?

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 52

In a methane

(C H_{4})

molecule, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the centre. In coordinates where one of the

C - H

bonds is in the direction of

\hat{i} + \hat{j} + \hat{k}

, an adjacent

C - H

bond is in the

\hat{i} - \hat{j} - \hat{k}

direction. Then, the angle between these two bonds is,

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 53

Consider east as positive

x -axis

and north as positive

y -axis

. A girl walks

10 m

east first, then

10 m

in a direction

30 °

west of north for the second time and then third time in unknown direction and magnitude to return to her initial position. What is her third displacement in unit vector notation?

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 54

A sail boat sails

2 km

due east,

5 km

37 °

south of east and finally an unknown displacement. If the final displacement of the boat from the starting point is

6 km

due east, determine the third displacement.

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 55

Two horizontal forces of magnitudes $10 N$ and $P N$ act on a particle. The force of magnitude $10 N$ acts due west and the force of magnitude $P N$ acts on a bearing of $30^{°}$ east of north as shown in figure. The resultant of these two force acts due north. Find the magnitude of the resultant.

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>Exercises>Q 56

A particle whose speed is

50 m s^{- 1}

moves along the line from

A (2, 1)

B (9, 25)

. Find its velocity vector in the form of

a \hat{i} + b \hat{j}

The resultant of three vectors 1, 2 and 3 units whose directions are those of the sides of an equilateral triangle is at an angle of,

Important Questions on Vectors

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The resultant of three vectors $1$ , $2$ and $3$ units whose directions are those of the sides of an equilateral triangle is at an angle of,