Determine whether each pair of vectors is orthogonal.
〈1...

Question

Determine whether each pair of vectors is orthogonal.

〈1, 1〉, 〈1, -1〉

Accepted Answer

Hello, today we are going to be checking whether the given vectors are orthogonal. We are given the vector 13 comma 13 and the vector 13 comma negative 13. So how can we tell if these two vectors are orthogonal or not? While the definition of orthogonality states that if the dot product of both of these vectors is equal to zero, then these vectors are orthogonal. If they are equal to any value that is not zero, then they are not orthogonal. We're going to set the first vector equal to you. You will be equal to 1313. We are going to set a second vector V equal to the second given vector which is 13 comma negative 13. Using the definition of the dot product, the dot product of U do V is equal to the product of the X components of the vectors which will be 13 multiplied by 13 plus the product of the Y components of the vectors which will be 13 and negative 13, 13 multiplied by 13 will give us the value of 169 and 13 multiplied by negative 13 will give us the value of negative 169 169 plus negative 169 will leave us with a sum of zero. So that means the dot product between the two vectors is equal to zero, proving that the two vectors are orthogonal to each other. And with that being said, the answer to this problem is going to be a they are orthogonal. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Struggling with Trigonometry?

Determine whether each pair of vectors is orthogonal.
〈1, 1〉, 〈1, -1〉

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Struggling with Trigonometry?

Determine whether each pair of vectors is orthogonal.〈1, 1〉, 〈1, -1〉

Watch next

Dot Product practice set

Determine whether each pair of vectors is orthogonal.
〈1, 1〉, 〈1, -1〉