JEE Exam > JEE Questions > Unit vector are makes angle pi by 3 and Pi by...
Start Learning for Free
Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta?
Most Upvoted Answer
Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respe...
Understanding Unit Vectors
Unit vectors are vectors with a magnitude of 1 that indicate direction. In this case, we need to find the angle θ that a certain unit vector makes with the I-cap vector (the x-axis), given its angles with the J-cap (y-axis) and K-cap (z-axis).
Given Angles
- The unit vector makes an angle of π/3 with the J-cap.
- The unit vector makes an angle of π/2 with the K-cap.
Components of the Unit Vector
Let the unit vector be represented as V = (a, b, c) where:
- a = x-component (I-cap)
- b = y-component (J-cap)
- c = z-component (K-cap)
From the information provided, we can derive the following:
- The relationship with J-cap:
- cos(π/3) = b/|V|
- Since |V| = 1, b = cos(π/3) = 1/2
- The relationship with K-cap:
- cos(π/2) = c/|V|
- Since |V| = 1, c = cos(π/2) = 0
Now, since |V| = 1, we have:
- a^2 + (1/2)^2 + 0^2 = 1
- a^2 + 1/4 = 1
- a^2 = 3/4
- a = √(3/4) = √3/2
Final Unit Vector
Thus, the unit vector is:
V = (√3/2, 1/2, 0)
Calculating Angle θ
To find the acute angle θ with the I-cap:
- cos(θ) = a/|V| = (√3/2)/1 = √3/2
- Therefore, θ = π/6 (30 degrees)
Conclusion
The acute angle θ that the unit vector makes with the I-cap is π/6 radians or 30 degrees.
Unit vectors are vectors with a magnitude of 1 that indicate direction. In this case, we need to find the angle θ that a certain unit vector makes with the I-cap vector (the x-axis), given its angles with the J-cap (y-axis) and K-cap (z-axis).
Given Angles
- The unit vector makes an angle of π/3 with the J-cap.
- The unit vector makes an angle of π/2 with the K-cap.
Components of the Unit Vector
Let the unit vector be represented as V = (a, b, c) where:
- a = x-component (I-cap)
- b = y-component (J-cap)
- c = z-component (K-cap)
From the information provided, we can derive the following:
- The relationship with J-cap:
- cos(π/3) = b/|V|
- Since |V| = 1, b = cos(π/3) = 1/2
- The relationship with K-cap:
- cos(π/2) = c/|V|
- Since |V| = 1, c = cos(π/2) = 0
Now, since |V| = 1, we have:
- a^2 + (1/2)^2 + 0^2 = 1
- a^2 + 1/4 = 1
- a^2 = 3/4
- a = √(3/4) = √3/2
Final Unit Vector
Thus, the unit vector is:
V = (√3/2, 1/2, 0)
Calculating Angle θ
To find the acute angle θ with the I-cap:
- cos(θ) = a/|V| = (√3/2)/1 = √3/2
- Therefore, θ = π/6 (30 degrees)
Conclusion
The acute angle θ that the unit vector makes with the I-cap is π/6 radians or 30 degrees.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta?
Question Description
Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta?.
Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta?.
Solutions for Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? defined & explained in the simplest way possible. Besides giving the explanation of
Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta?, a detailed solution for Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? has been provided alongside types of Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? theory, EduRev gives you an
ample number of questions to practice Unit vector are makes angle pi by 3 and Pi by 2 with J and K cap respectively and an acute angle theta with I find theta? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup