In Exercises 40–41, use the dot product to determine whether v an...

Question

In Exercises 40–41, use the dot product to determine whether v and w are orthogonal.v = 12i - 8j, w = 2i + 3j

Accepted Answer

Hello, today we're going to be determining whether the two given vectors are orthogonal to each other. So we are told that vector A is defined as 13 I minus J. And we are told that vector B is defined as three I plus 39 J. In order to determine whether these two vectors are orthogonal to each other. We'll need to calculate the dot product of A and B. And if that dot product is equal to zero, that will show that the two vectors are orthogonal to each other. So let's calculate the dot product of A and B. In order to get the dot product, we'll multiply the I components of the A and B vector together and multiply the J components of the A and B vector together. Then we're going to want to take the sum of the two products. So the dot product of A and B is going to equal to 13, multiplied by three plus negative one multiplied by 39 13, multiplied by three will give us the value of 39 negative one multiplied by 39 will give us the value of negative 39. Finally, 39 minus 39 is equal to zero. What this means is that the dot product of the given vectors A and B is equal to zero. And this shows that the two given vectors are orthogonal to each other. And with that being said, the answer to this problem is going to be A. 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.

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In Exercises 40–41, use the dot product to determine whether v and w are orthogonal.v = 12i - 8j, w = 2i + 3j

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