NEET Exam > NEET Questions > If a (a vector) and b (b vector) are 2 non co...
Start Learning for Free
If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution?
Verified Answer
If a (a vector) and b (b vector) are 2 non collinear unit vectors and ...
This question is part of UPSC exam. View all NEET courses
Most Upvoted Answer
If a (a vector) and b (b vector) are 2 non collinear unit vectors and ...
Given:
- Two non-collinear unit vectors: a and b
- |a b| = √3 (magnitude of the vector formed by concatenating a and b)
To find:
The value of (a - b).(2a + b)
Solution:
Step 1: Find the dot product of (a - b) and (2a + b)
Let's expand the dot product expression:
(a - b).(2a + b) = 2a.a + a.b - 2b.a - b.b
Step 2: Simplify the dot product expression using the properties of dot product
As a and b are both unit vectors, their magnitudes are 1.
2a.a = 2|a|^2 = 2(1) = 2
a.b = |a| |b| cosθ
Since a and b are non-collinear, the angle between them is 90 degrees (π/2 radians). Therefore, cosθ = 0.
2b.a = 2|b|^2 = 2(1) = 2
b.b = |b|^2 = 1
Substituting the values back into the dot product expression:
(a - b).(2a + b) = 2 + 0 - 2 + 1
Simplifying further:
(a - b).(2a + b) = 1
Step 3: Conclusion
The value of (a - b).(2a + b) is 1.
- Two non-collinear unit vectors: a and b
- |a b| = √3 (magnitude of the vector formed by concatenating a and b)
To find:
The value of (a - b).(2a + b)
Solution:
Step 1: Find the dot product of (a - b) and (2a + b)
Let's expand the dot product expression:
(a - b).(2a + b) = 2a.a + a.b - 2b.a - b.b
Step 2: Simplify the dot product expression using the properties of dot product
As a and b are both unit vectors, their magnitudes are 1.
2a.a = 2|a|^2 = 2(1) = 2
a.b = |a| |b| cosθ
Since a and b are non-collinear, the angle between them is 90 degrees (π/2 radians). Therefore, cosθ = 0.
2b.a = 2|b|^2 = 2(1) = 2
b.b = |b|^2 = 1
Substituting the values back into the dot product expression:
(a - b).(2a + b) = 2 + 0 - 2 + 1
Simplifying further:
(a - b).(2a + b) = 1
Step 3: Conclusion
The value of (a - b).(2a + b) is 1.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution?
Question Description
If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution?.
If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution?.
Solutions for If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? defined & explained in the simplest way possible. Besides giving the explanation of
If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution?, a detailed solution for If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? has been provided alongside types of If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? theory, EduRev gives you an
ample number of questions to practice If a (a vector) and b (b vector) are 2 non collinear unit vectors and |a + b| = √3, then find the value of (a - b).(2a+b)?please give the solution? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET 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