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Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b?
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Two vectors a and b are inclined to each other at an angle theta . Whi...
Unit vector perpendicular to two vectors a and b
When two vectors are inclined to each other at an angle theta, we can find the unit vector perpendicular to both vectors a and b by using the cross product.
Cross product of vectors a and b
The cross product of vectors a and b is a vector that is perpendicular to both a and b. The magnitude of the cross product is given by:
|a x b| = |a| |b| sin(theta)
where |a| and |b| are the magnitudes of vectors a and b, and theta is the angle between them.
Unit vector perpendicular to vectors a and b
The unit vector perpendicular to vectors a and b is given by:
n = (a x b) / |a x b|
where n is the unit vector perpendicular to a and b, and |a x b| is the magnitude of the cross product of vectors a and b.
Example
Suppose vectors a and b are given by:
a = 2i + 3j + 4k
b = 3i - 2j + k
To find the unit vector perpendicular to vectors a and b, we first need to find the cross product:
a x b = (10i - 5j - 13k)
The magnitude of the cross product is:
|a x b| = sqrt(10^2 + (-5)^2 + (-13)^2) = sqrt(210)
Therefore, the unit vector perpendicular to vectors a and b is:
n = (10i - 5j - 13k) / sqrt(210) = (2sqrt(210)/21)i - (sqrt(210)/21)j - (3sqrt(210)/21)k
Community Answer
Two vectors a and b are inclined to each other at an angle theta . Whi...
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Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b?
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Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b?.
Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vectors a and b are inclined to each other at an angle theta . Which of the following is the unit vector perpendicular to both vector a and b?.
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