Class 10 Exam > Class 10 Questions > 23. Express the vector in the Cartesian form ...
Start Learning for Free
23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N?
Most Upvoted Answer
23. Express the vector in the Cartesian form if the angle made by it w...
To express a vector in Cartesian form, we need to find its components along the x, y, and z axes. We are given that the vector makes an angle of 60° with the y-axis and 45° with the z-axis. Let's break down the problem step by step.
Magnitude of the force: 200N
Angle with the y-axis: 60°
Angle with the z-axis: 45°
Finding the x-component:
The x-component of the vector can be found using trigonometry. Since the angle with the x-axis is not given, let's assume it to be 'a'. The x-component can be found using the formula:
x = magnitude * cos(angle)
x = 200N * cos(a)
Finding the y-component:
The y-component can be found using trigonometry. The angle with the y-axis is given as 60°. The y-component can be found using the formula:
y = magnitude * sin(angle)
y = 200N * sin(60°)
y = 200N * √3/2
y = 100√3 N
Finding the z-component:
The z-component can be found using trigonometry. The angle with the z-axis is given as 45°. The z-component can be found using the formula:
z = magnitude * sin(angle)
z = 200N * sin(45°)
z = 200N * √2/2
z = 100√2 N
Expressing the vector in Cartesian form:
The vector can now be expressed in Cartesian form as the sum of its components along the x, y, and z axes:
Vector = x î + y ĵ + z k̂
Substituting the values:
Vector = (200N * cos(a)) î + (100√3 N) ĵ + (100√2 N) k̂
Simplifying the expression:
Vector = 200 cos(a) î + 100√3 ĵ + 100√2 k̂
Therefore, the vector can be expressed in Cartesian form as 200 cos(a) î + 100√3 ĵ + 100√2 k̂.
Magnitude of the force: 200N
Angle with the y-axis: 60°
Angle with the z-axis: 45°
Finding the x-component:
The x-component of the vector can be found using trigonometry. Since the angle with the x-axis is not given, let's assume it to be 'a'. The x-component can be found using the formula:
x = magnitude * cos(angle)
x = 200N * cos(a)
Finding the y-component:
The y-component can be found using trigonometry. The angle with the y-axis is given as 60°. The y-component can be found using the formula:
y = magnitude * sin(angle)
y = 200N * sin(60°)
y = 200N * √3/2
y = 100√3 N
Finding the z-component:
The z-component can be found using trigonometry. The angle with the z-axis is given as 45°. The z-component can be found using the formula:
z = magnitude * sin(angle)
z = 200N * sin(45°)
z = 200N * √2/2
z = 100√2 N
Expressing the vector in Cartesian form:
The vector can now be expressed in Cartesian form as the sum of its components along the x, y, and z axes:
Vector = x î + y ĵ + z k̂
Substituting the values:
Vector = (200N * cos(a)) î + (100√3 N) ĵ + (100√2 N) k̂
Simplifying the expression:
Vector = 200 cos(a) î + 100√3 ĵ + 100√2 k̂
Therefore, the vector can be expressed in Cartesian form as 200 cos(a) î + 100√3 ĵ + 100√2 k̂.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N?
Question Description
23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N?.
23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N?.
Solutions for 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? defined & explained in the simplest way possible. Besides giving the explanation of
23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N?, a detailed solution for 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? has been provided alongside types of 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? theory, EduRev gives you an
ample number of questions to practice 23. Express the vector in the Cartesian form if the angle made by it with y-axis and z-axis are 60° and 45° respectively. Also, it makes an angle of a with the x-axis. The magnitude of the force is 200N. (a) 100 - 100; 141.4k N (b) 100 100j 141.4k N (c) 100 - 100 - 141.4k N (d) 100i 100; - 141.4k N? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup