# 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

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

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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.

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