In Exercises 23–32, use the dot product to determine whether v an...

Question

In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.

v = 2i + 8j, w = 4i - j

Accepted Answer

Hello. Today we're going to be proving whether the vectors A and B are orthogonal to each other. So how do we show that two vectors are orthogonal? Well, if we take the dot product of both of the vectors and the dot product is equal to zero, that shows that the two vectors are orthogonal to each other. So what we're going to need to do is we're going to need to calculate the dot product of A and B vector A is given to us as 12 I minus six J and vector B is given to us as five I plus 10 J. In order to calculate the dot product of A and B, we're going to need to take the product of the I components and J components together then take the sum of both of the products. So the dot product of A and B is gonna be defined as multiplied by five plus negative six, multiplied by 10, 12 multiplied by five will give us the value of 60 and negative six multiplied by 10 will give us the value of negative 60. Finally, 60 minus 60 will give us the value of zero. And what this means is that the dot product of A and B is equal to zero, which proves that the two 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 23–32, use the dot product to determine whether v and w are orthogonal. v = 2i + 8j, w = 4i - j