Question Video: Adding Vectors Using a Grid | Nagwa Question Video: Adding Vectors Using a Grid | Nagwa

Question Video: Adding Vectors Using a Grid Physics • First Year of Secondary School

Which of the vectors 𝐏, 𝐐, 𝐑, 𝐒, or 𝐓 shown in the diagram is equal to 𝐀 + 𝐁?

01:37

Video Transcript

Which of the vectors 𝐏, 𝐐, 𝐑, 𝐒, or 𝐓 shown in the diagram is equal to 𝐀 plus 𝐁?

So here we have a diagram showing us seven vectors, including the vectors 𝐀 and 𝐁. And we’re being asked, of the other five vectors 𝐏, 𝐐, 𝐑, 𝐒, and 𝐓, which one will be equal to the sum of 𝐀 and 𝐁. Since the vectors have been given to us in a graphical form — they’re represented by the blue arrows — we can add them together graphically using the tip-to-tail method. In the tip-to-tail method, one vector slides over until its tail is on the tip of the other vector. The resultant is drawn from the tail of the unmoved vector to the tip of the moved vector.

In our problem, we want to add together the vectors 𝐀 and 𝐁. So let’s keep the vector 𝐀 stationary and slide the vector 𝐁 over so that its tail rests on the tip of vector 𝐀, making sure that both the horizontal and vertical components of vector 𝐁 as we’ve drawn it now are the same as the original vector 𝐁. In this case, the horizontal component is two units to the right and the vertical component is three units upward. We can now draw on the resultant vector, that is, the vector which is equivalent to 𝐀 plus 𝐁. This is drawn from the tail of the unmoved vector 𝐀 to the tip of the moved vector 𝐁.

We can see that this resultant vector has the same direction and magnitude as the vector 𝐐. In other words, it’s equal to vector 𝐐. This means that vector 𝐐 is equal to the sum of 𝐀 and 𝐁. Of the five vectors drawn in the diagram, 𝐏, 𝐐, 𝐑, 𝐒, and 𝐓, it’s vector 𝐐 that’s equal to 𝐀 plus 𝐁.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy