At what angle should the two force vectors 2 F and 2 F act so that the resultant force is 10 F ?

Let there are two force vectors A and B at the angle of θ to each other. A = 2 F and B = 2 F The resultant of two vectors is R = A 2 + B 2 + 2 A · B cos θ . Given that resultant force is R = 10 F . Putting the value of A , B and R in the above expression, 10 F = 2 F 2 + 2 F 2 + 2 2 F · 2 F cos θ Squaring both the sides of the equation, 10 F 2 = 4 F 2 + 2 F 2 + 4 2 F 2 cos θ ⇒ 4 F 2 = 4 2 F 2 cos θ ⇒ cos θ = 1 2 ⇒ θ = 45 °

At what angle should the two force vectors 2 F and 2 F act so that the resultant force is 10 F ?

Let there are two force vectors A and B at the angle of θ to each other. A = 2 F and B = 2 F The resultant of two vectors is R = A 2 + B 2 + 2 A · B cos θ . Given that resultant force is R = 10 F . Putting the value of A , B and R in the above expression, 10 F = 2 F 2 + 2 F 2 + 2 2 F · 2 F cos θ Squaring both the sides of the equation, 10 F 2 = 4 F 2 + 2 F 2 + 4 2 F 2 cos θ ⇒ 4 F 2 = 4 2 F 2 cos θ ⇒ cos θ = 1 2 ⇒ θ = 45 °

The resultant of two forces has magnitude 20 N . One of the forces is of magnitude 20 3 N and makes an angle of 30 ° with the resultant. Then what is the magnitude of the other force?

Let A = 20 3 N be the known force, B be the unknown force and R = 20 N is the resultant of them. From triangular law of vector addition, A → + B → = R → ⇒ B → = R → - A → ⇒ B = R 2 + A 2 - 2 R A cos θ ⇒ B 2 = 20 3 2 + 20 2 - 2 20 20 3 cos 30 ° ⇒ B 2 = 1600 - 1200 = 400 or B = 20 N

If A → = 4 i ^ - 3 j ^ and B → = 6 i ^ + 8 j ^ , then find the magnitude and direction of A → + B → .

There are given two vectors A → and B → . A → = 4 i ^ - 3 j ^ and B → = 6 i ^ + 8 j ^ Vector sum of these vectors is S → = A → + B → S → = 4 i ^ - 3 j ^ + 6 i ^ + 8 j ^ = 10 i ^ + 5 j ^ The magnitude of this sum vector, S → = A → + B → = 10 2 + 5 2 S → = 125 = 5 5 The direction of the sum vector, tan θ = Y component X component = 5 10 ⇒ θ = tan - 1 1 2

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At what angle should the two force vectors $2 F$ and $\sqrt{2} F$ act so that the resultant force is $\sqrt{10} F$ ?

Important Questions on Vectors

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.2>Q 8

Two forces while acting on a particle in opposite directions have the resultant of

10 N

. If they act at right angles to each other, the resultant is found to be

50 N

. Find the two forces.

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.2>Q 9

Two forces each equal

\frac{F}{2}

act at right angle. Their effect may be neutralized by a third force acting along their bisector in the opposite direction. What is the magnitude of the third force?

EASY

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.2>Q 10

The resultant of two forces has magnitude

20 N

. One of the forces is of magnitude

20 \sqrt{3} N

and makes an angle of

30 °

with the resultant. Then what is the magnitude of the other force?

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.3>Q 1

A car travels $6 km$ towards north at an angle of $45 °$ to the east and then travels distance of $4 km$ towards north at an angle of $135 °$ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final position makes with the east?

Question Image

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.3>Q 2

\vec{A} = 4 \hat{i} - 3 \hat{j}

and

\vec{B} = 6 \hat{i} + 8 \hat{j}

, then find the magnitude and direction of

\vec{A} + \vec{B}

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.3>Q 3

A truck travelling due north at

20 m s^{- 1}

turns west and travels at the same speed. Find the change in its velocity.

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.3>Q 4

If the sum of two unit vectors is a unit vector, then find the magnitude of difference.

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.3>Q 5

Two forces

F_{1} = 1 N

and

F_{2} = 2 N

act along the lines

x = 0

and

y = 0

, respectively. Then find the resultant of forces.

At what angle should the two force vectors 2F and 2F act so that the resultant force is 10F?

Important Questions on Vectors

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At what angle should the two force vectors $2 F$ and $\sqrt{2} F$ act so that the resultant force is $\sqrt{10} F$ ?