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

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

Let A → = 2 i ^ + j ^ , B → = 3 j ^ - k ^ and C → = 6 i ^ - 2 k ^ . Find the value of A → - 2 B → + 3 C → .

Given three vectors, A → , B → and C → . A → = 2 i ^ + j ^ , B → = 3 j ^ - k ^ , C → = 6 i ^ - 2 k ^ . Let, R → = A → - 2 B → + 3 C → . Putting values of all the vectors in the above expression, R → = A → - 2 B → + 3 C → = 2 i ^ + j ^ - 2 3 j ^ - k ^ + 3 6 i ^ - 2 k ^ , ⇒ R → = 2 i ^ + j ^ - 6 j ^ + 2 k ^ + 18 i ^ - 6 k ^ = 20 i ^ - 5 j ^ - 4 k ^ . Hence, the resultant value of the given expression is 20 i ^ - 5 j ^ - 4 k ^ .

E M B I B E

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

EASY

JEE Advanced

IMPORTANT

Earn 100

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?

Important Questions on Vectors

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?

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MEDIUM

JEE Advanced

IMPORTANT

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

If

\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.

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.3>Q 6

Let

\vec{A} = 2 \hat{i} + \hat{j}

,

\vec{B} = 3 \hat{j} - \hat{k}

and

\vec{C} = 6 \hat{i} - 2 \hat{k}

. Find the value of

\vec{A} - 2 \vec{B} + 3 \vec{C}

.

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 3 - Vectors>CONCEPT APPLICATION EXERCISE 3.3>Q 7

An object of $m kg$ with speed of $v m s^{- 1}$ strikes a wall at an angle $θ$ and rebounds at the same speed and same angle. Find the magnitude of change in the momentum of the object.

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