Question Video: Differentiating between Scalar and Vector Quantities Physics • 9th Grade

If an area is multiplied by a length, is the resultant quantity a vector quantity or a scalar quantity?

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Video Transcript

If an area is multiplied by a length, is the resultant quantity a vector quantity or a scalar quantity?

All right, so we’re talking about multiplying an area by a length. And we could imagine, say, that this is our area and that this here is our length. When we multiply this area by this length, we’re going to get some result, and we want to know whether that’s a vector quantity or a scalar quantity. Here’s the difference between the two. A scalar quantity, or scalar for short, has a magnitude only, while a vector quantity, or a vector, has both magnitude and direction. So, to figure out whether our area multiplied by a length is a scalar or a vector, we’ll need to see whether it has a magnitude only or a magnitude along with a direction.

The product of our area and our length is this volume 𝑉. And so now we ask ourselves, does this volume have a magnitude only or does it have a magnitude along with a direction? Put that way, we can see that this volume does have a magnitude, that is, a size, that’s equal to whatever 𝐴 times 𝐿 is. But there’s no particular direction in which this volume or any volume points. So here, we do have a magnitude, but we don’t have a direction. Based on our definitions of scalar and vector quantities, that then answers our question. If an area is multiplied by a length, the resultant quantity is a scalar quantity.

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