Find the value of k for which the vectors  vector x=  0                                      vector y =    0...

Find the value of k for which the vectors

 

vector x=  0                                      vector y =    0

               -1                                                          0

                2                  and                                  -1

               -3                                                          k

These two vectors are orthogonal

Expert Answers
lfryerda eNotes educator| Certified Educator

Any two vectors are orthogonal when the dot product of the two vectors is zero.  The dot product is the sum of the components multiplied together.  That is:

`x circ y=0(0)-1(0)+2(-1)-3k`

`=-2-3k`

Setting the dot product equal to zero and solving for k gets:

`-2-3k=0`  solve

`3k=-2`  divide by 3

`k=-2/3`

The value `k=-2/3` makes the vectors orthogonal.