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

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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

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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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