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If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ?
Most Upvoted Answer
If magnitudes of a vector and b vector are 10 units and 6 units respec...
Given:
To find: Angle between vector (a-b) and vector a
Solution:
To find the angle between (a-b) and a, we first need to find the vector (a-b).
Method 1: Using Parallelogram Law of Vector Addition
Method 2: Using Component Method
Using either method, we get vector (a-b) as follows:
Now, we need to find the angle between (a-b) and a. Let this angle be x.
Using dot product formula, we get:
a . (a-b) = |a||a-b|cos(x)
=> 10*4*cos(x) = 100
=> cos(x) = 0.25
=> x = cos^-1(0.25) = 75.52 degrees
Therefore, the angle between vector (a-b) and vector a is 75.52 degrees.
- Magnitude of vector a = 10 units
- Magnitude of vector b = 6 units
- Angle between a and b = 60 degrees
To find: Angle between vector (a-b) and vector a
Solution:
To find the angle between (a-b) and a, we first need to find the vector (a-b).
Method 1: Using Parallelogram Law of Vector Addition
- Draw vectors a and b with their tails meeting at a common point O.
- Complete the parallelogram with sides a and b.
- The diagonal of the parallelogram passing through O is vector (a-b).
Method 2: Using Component Method
- Express vectors a and b in terms of their components.
- Subtract the corresponding components of a and b to get the components of (a-b).
- Express the resultant vector (a-b) in terms of magnitude and direction.
Using either method, we get vector (a-b) as follows:
- Magnitude of vector (a-b) = sqrt(10^2 + 6^2 - 2*10*6*cos(60)) = 4 units
- Direction of vector (a-b) = tan^-1((6*sin(60)) / (10 - 6*cos(60))) = 123.69 degrees
Now, we need to find the angle between (a-b) and a. Let this angle be x.
Using dot product formula, we get:
a . (a-b) = |a||a-b|cos(x)
=> 10*4*cos(x) = 100
=> cos(x) = 0.25
=> x = cos^-1(0.25) = 75.52 degrees
Therefore, the angle between vector (a-b) and vector a is 75.52 degrees.
Community Answer
If magnitudes of a vector and b vector are 10 units and 6 units respec...
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If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ?
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If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ?.
If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If magnitudes of a vector and b vector are 10 units and 6 units respectively and angle between them is 60,then find the angle between (a-b) vector and a vector ?.
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