Question 1011207: Find a vector perpendicular to the given vector 2i+9j-6k
Please Show all your work step by step.
Answer by mathmate(429)   (Show Source):
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Question:
Find a vector perpendicular to the given vector 2i+9j-6k
Please Show all your work step by step.
Solution:
A vector will be denoted where x,y,z are the respective components.
We're looking for a vector perpendicular to P=<2,9,-6>.
In fact, there is an infinite number of vectors perpendicular to P.
We know that the cross product of two non-parallel vectors P, Q is perpendicular to both P and Q.
So by finding the cross product P and an arbitrary vector Q=, we can obtain the vector R=PxQ such that R is perpendicular to both P and Q, with the restriction that Q is not parallel to P, or Q does not equal kQ where k is a real number.
The cross product can be obtained by evaluation of the determinant
|i j k |
|2 9 -6|
|a b c |
which gives R=<9c+6b, -2c-6a, 2b-9a>
Thus
R=<9c+6b, -2c-6a, 2b-9a> is a vector perpendicular to P=<2,9,-6> for any vector Q= such that Q≠kP and k is a real number.
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