# 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

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Expert Answers

lfryerda | 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.**