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A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is?
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A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is?
Finding a Vector Perpendicular to Both Given Vectors
To find a vector perpendicular to both the vector 2i^-j^ 5k^ and the x-axis, we can use the cross product of the two vectors.
Steps to Find the Cross Product
- First, we need to write the two vectors in their component form, which is:
- Next, we can find the cross product of the two vectors by using the following formula:
- Substituting the values of a and b into the formula, we get:
- This simplifies to:
- Therefore, a vector perpendicular to both the vector 2i^-j^ 5k^ and the x-axis is:
a = 2i^-j^ + 5k^
b = xi^ + 0j^ + 0k^
a x b = (a2b3 - a3b2)i^ + (a3b1 - a1b3)j^ + (a1b2 - a2b1)k^
a x b = (5)(0) - (0)(0)i^ + (0)(2) - (2)(0)j^ + (2)(0) - (5)(x)k^
a x b = -5xk^
v = -5k^
Explanation
The cross product of two vectors gives us a vector that is perpendicular to both of the original vectors. In this case, we have one vector that lies in the x-y plane (2i^-j^), and one vector that lies entirely along the x-axis (xi^). Therefore, the cross product between these two vectors will be a vector that only has a z-component, which means it is perpendicular to both of the original vectors.
By finding the cross product using the formula, we get a vector that is proportional to -5k^. This means that any scalar multiple of this vector (e.g. -10k^, 5k^, etc.) will also be perpendicular to both of the original vectors.
Community Answer
A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is?
In x axis , 2i^
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A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is?
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A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis 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 A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is?.
A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis 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 A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector perpendicular to both the vector 2i^-j^ 5k^ and x axis is?.
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