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The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.?
Most Upvoted Answer
The resultant of two vectors a and b of magnitudes 6 and 10 respective...
Problem:
The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.
Solution:
Given, magnitudes of vectors a and b are 6 and 10 respectively.
Let the angle between vectors a and b be θ.
Let's assume vector a is in the direction of x-axis.
The magnitude of the resultant R is given by the Pythagorean theorem as:
R² = a² + b²
R² = 6² + 10²
R² = 136
R = √136
R = 2√34
Let's assume vector b is at an angle of θ with the positive x-axis.
The dot product of vectors a and b is given by:
a . b = |a| |b| cosθ
Since a and b are at right angles, cosθ = 0
Therefore, a . b = 0
The dot product of vectors a and b can also be written as:
a . b = ax bx + ay by
where ax and ay are the components of vector a and bx and by are the components of vector b.
Since a is in the direction of x-axis, its components are ax = 6 and ay = 0.
Therefore, a . b = 6bx
Substituting a . b = 0, we get:
6bx = 0
bx = 0
This implies that vector b is in the direction of y-axis.
Therefore, the angle between vectors a and b is 90 degrees.
Answer:
The magnitude of the resultant of vectors a and b is 2√34 and the angle between the vectors is 90 degrees.
The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.
Solution:
Given, magnitudes of vectors a and b are 6 and 10 respectively.
Let the angle between vectors a and b be θ.
Let's assume vector a is in the direction of x-axis.
The magnitude of the resultant R is given by the Pythagorean theorem as:
R² = a² + b²
R² = 6² + 10²
R² = 136
R = √136
R = 2√34
Let's assume vector b is at an angle of θ with the positive x-axis.
The dot product of vectors a and b is given by:
a . b = |a| |b| cosθ
Since a and b are at right angles, cosθ = 0
Therefore, a . b = 0
The dot product of vectors a and b can also be written as:
a . b = ax bx + ay by
where ax and ay are the components of vector a and bx and by are the components of vector b.
Since a is in the direction of x-axis, its components are ax = 6 and ay = 0.
Therefore, a . b = 6bx
Substituting a . b = 0, we get:
6bx = 0
bx = 0
This implies that vector b is in the direction of y-axis.
Therefore, the angle between vectors a and b is 90 degrees.
Answer:
The magnitude of the resultant of vectors a and b is 2√34 and the angle between the vectors is 90 degrees.
Community Answer
The resultant of two vectors a and b of magnitudes 6 and 10 respective...
Resultant of a and b, R=(a+b)
As per Q,
R•a=0 [dot product]
(a+b)•a =0
a•a + b•a =0
|a|² + b•a =0
6² + 60 cosx =0
or cosx = - ⅗
or x = (180 - 53) [ cos is -ve, it must lie in 2nd or 3rd quad]
or x = 127 deg
As per Q,
R•a=0 [dot product]
(a+b)•a =0
a•a + b•a =0
|a|² + b•a =0
6² + 60 cosx =0
or cosx = - ⅗
or x = (180 - 53) [ cos is -ve, it must lie in 2nd or 3rd quad]
or x = 127 deg
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The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.?
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The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.?.
The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resultant of two vectors a and b of magnitudes 6 and 10 respectively is at right angles to the vector a. Find their resultant and also the angle between the given vectors.?.
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