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 = 3i, w = -4j

Accepted Answer

Hello, today we're going to be determining whether the two vectors A and B are orthogonal to each other. So what does it mean for two vectors to be orthogonal? Well, if the dot product of A and B is equal to zero, then A and B are going to be orthogonal to each other. So in order to determine this value, we'll need to first take the dot product of A and B. Now the vector A is given to us as 21 I. But notice that the vector A is missing AJ component, we can represent this J component with a coefficient of zero and we can rewrite the vector A as 21 I plus zero. J. Next notice that the B vector is missing the I component. We can rewrite the I component with the coefficient of zero and rewrite the B vector as zero I minus J. Now, in order to take the dot product of A and B, we're going to be adding the sums of the product of the I components and J components together. So the dot product of A and B is going to be 21 multiplied by zero plus zero, multiplied by negative 14. Now anything multiplied by zero will give us zero. So what we are left with is zero plus zero, which is equal to zero. And what this means is that the dot product of A and B is equal to zero. Thus 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. 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?

In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.v = 3i, w = -4j

Watch next

Dot Product practice set