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## Class 11 Physics (India)

### Course: Class 11 Physics (India)>Unit 8

Lesson 3: Review: Unit vectors

# Unit vectors and engineering notation

Using unit vectors to represent the components of a vector. Created by Sal Khan.

## Want to join the conversation?

• Is there any video where Sal explains why vector v is the sum of vector vx and vector vy. If there is can anyone link it.
• To correct the misconception. V = Vx + Vy, the sum of its components. But the magnitude ||V||^2 = ||Vx||^2 + ||Vy||^2, that's where Pythagoras' theorem comes into place.

An example, say you have a displacement S.
S = 3i + 4j
This means that it moves 3 units in the right direction, and 4 units in the up direction.
The components of this are:
Sx = 3i
Sy = 4j

What is confusing is that the magnitude of the displacement S is not equal to 3 + 4. The magnitude is 5 (sqrt(3^2 + 4^2) = sqrt(25)).

The confusion comes from the relationship of the size of the components and the magnitude. The video where he explains this can be found here: https://www.khanacademy.org/science/physics/two-dimensional-motion/two-dimensional-projectile-mot/v/visualizing-vectors-in-2-dimensions
• how is v=vx+vy = 5square3i+5j? shouldnt we use the pythagorens theroem to solve for v? I am confused.
• In the video of intrduction of vector it is specified that a two dimensional vector is equal to the sum of two one dimensional vectors, and when he is using the unit vectors it is transforming the units to vectors, and because of that the vector V is equal to the sum of vector Vx and Vy
• I thought vector v is equal to sqrt of vx^2 + vy^2
• Check out the 'Vectors' playlist in the Pre-calculus section to know the difference between adding vectors and finding the magnitude of a resultant vector.
• is there a video where i can learn how to find resultant vectors
• at , why is vector V= Vx+Vy??
isn't it the hypotenuse so shouldn't it be c^2 = a^2+b^2
• It is true that the length of the resultant vector (the magnitude of the vector) is calculated by the C^2=a^2+b^2, but getting to the vector position can be achieved either by traveling at the angle for the vector magnitude, or by splitting the position into x and y components and traveling along each axis for the individual lengths. It will take longer, given the same speed, if that is what you are interested in, but the "superposition" of being able to add individual x and y components is a key element in vector math. For example, when a baseball is hit it is leaving at an angle, but it has both x and y components that are separate (orthagonal!). If you are traveling along in a car, your vector for velocity will be (virtually) all in X, so Vy will be ~0. If you throw a ball into the air, its vector will be all Y, or Vy. The resultant vector on the ball will be Vx + Vy. And if you throw the ball in the same direction you are going, the vectors will add and you will get Vx(car) plus Vx(ball) for the total velocity.
• If 2 persons stretch a rope/string with a 100N force both then what will be the value of tension in the string??Explain.
• Tension is the force that the rope exerts on the bodies attached to it, so if each person is pulling the rope with a 100N force, the rope is also pulling each person with a 100N force (laws of Newton). The tension is, in this case, 100N.
• Starting at , why did he not use pythagorean theorem to describe V?
• Good question. The reason he said it this way is because he was referring to vectors and not the magnitude (length) of the vectors. If you want the magnitude, then you are correct in saying that you would need the Pythagorean theorem.
• Are there symbols like i hat and j hat that are in the negative direction or are they just -i and -j?
• -i would be in the negative direction of i. No need to define a new unit vector.
• Would it be wrong to factor out the 5 in the final description of the 2 dimensional vector to get 5(sqrt3i+j) ? Or is this not a good idea because it's just supposed to be notation and it's better off to keep your components as they are?
• I don't think it would be wrong, but it is good practice to keep the component vectors as they were. eg 5√3 i + 5 j.