Question 1011206
Do it like this one, done by tutor Mathmate.
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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&#8800;kP and k is a real number.