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the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is
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the resultant of two vectors a and b is perpendicular to the vector a ...
Given Information:
- Resultant of vectors a and b is perpendicular to vector a.
- Magnitude of resultant is half the magnitude of vector b.
- Angle between vectors a and b is to be found.
Explanation:
- Let the vectors a and b be represented as:
- Vector a = a
- Vector b = b
- Let the resultant vector be R.
- Given that R is perpendicular to a, we have:
- R . a = 0 (dot product is zero for perpendicular vectors)
- Given that magnitude of R is half the magnitude of b, we have:
- |R| = 0.5|b|
- The resultant vector R can be expressed as:
- R = a + b
- Using the properties of vectors, we can write:
- |R|^2 = |a|^2 + |b|^2 + 2|a||b|cos(theta) (where theta is the angle between a and b)
- Substituting the given values, we get:
- (0.5|b|)^2 = |a|^2 + |b|^2 + 2|a||b|cos(theta)
- 0.25|b|^2 = |a|^2 + |b|^2 + 2|a||b|cos(theta)
- 0.25 = (|a|/|b|)^2 + 1 + 2(|a|/|b|)cos(theta)
- From the above equation, we can solve for theta using trigonometric identities.
Conclusion:
- The angle between vectors a and b can be determined using the given information and trigonometric calculations.
- Resultant of vectors a and b is perpendicular to vector a.
- Magnitude of resultant is half the magnitude of vector b.
- Angle between vectors a and b is to be found.
Explanation:
- Let the vectors a and b be represented as:
- Vector a = a
- Vector b = b
- Let the resultant vector be R.
- Given that R is perpendicular to a, we have:
- R . a = 0 (dot product is zero for perpendicular vectors)
- Given that magnitude of R is half the magnitude of b, we have:
- |R| = 0.5|b|
- The resultant vector R can be expressed as:
- R = a + b
- Using the properties of vectors, we can write:
- |R|^2 = |a|^2 + |b|^2 + 2|a||b|cos(theta) (where theta is the angle between a and b)
- Substituting the given values, we get:
- (0.5|b|)^2 = |a|^2 + |b|^2 + 2|a||b|cos(theta)
- 0.25|b|^2 = |a|^2 + |b|^2 + 2|a||b|cos(theta)
- 0.25 = (|a|/|b|)^2 + 1 + 2(|a|/|b|)cos(theta)
- From the above equation, we can solve for theta using trigonometric identities.
Conclusion:
- The angle between vectors a and b can be determined using the given information and trigonometric calculations.
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the resultant of two vectors a and b is perpendicular to the vector a ...
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the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is
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the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is.
the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the resultant of two vectors a and b is perpendicular to the vector a and its magnitude is equal to half the magnitude of vector b. the angle between a and b is.
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