In Exercises 45–50, determine whether v and w are parallel, ortho...

Question

In Exercises 45–50, determine whether v and w are parallel, orthogonal, or neither.

v = 3i - 5j, w = 6i + 18 j
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Accepted Answer

Hello, today we're going to be determining whether the two given vectors are parallel or orthogonal. So we are told that vector A is defined as six I plus 11 J. And we are told that vector B is defined as five I minus 30/11 J. So we can start by checking whether the two vectors are orthogonal or not. In order to determine whether two vectors are orthogonal. We're going to take the dot product of those two vectors. And if the dot product of the two vectors equals to zero, then that proves that the two vectors are orthogonal. So let's start by determining the dot product. In order to take the dot product A dot B, we're going to multiply the I components together multiply the J components together then take the sum of the two products. So the dot product A dot B will be defined as six multiplied by five plus 11, multiplied by negative 30/11, six multiplied by five will give us the value of 30 and multiplied by negative 30/11 will give us the product of negative 30. Finally, 30 minus 30 will give us a final value of zero. So what this means is that the dot product A dot B is equal to zero. And this proves that the two vectors are orthogonal to each other. And with that being said, the answer to this problem is going to be B. 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.

In Exercises 45–50, determine whether v and w are parallel, orthogonal, or neither. v = 3i - 5j, w = 6i + 18 j 5

Key Concepts

Vector Operations

Dot Product

Parallel and Orthogonal Vectors

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