Q: Is it possible to add any two vector?

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Consider an equilateral triangle. If each vector started at the center of the triangle and went through a different vertex than the other two vectors then they would cancel. I believe in order for them to add to a null vector they must be co-planer.

No. The vector resultant of addition of vectors is the vector that would connect the tail of the first vector to the head of the last. For any set of vectors to add to the zero vector, the endpoint of the last vector added must be coincident with the start point of the first. Therefore for the sum of only two vectors to have a chance of being the zero vector, the second vector must be in a direction exactly opposite the first. So you can tell that the result of adding the two vectors could only can be zero vector if the two vectors were of two equal magnitude.

You get a third vector.

Yes, two vectors of similar kind can be added. For example we can add a distance vector with another distance vector. But we cannot add distance vector and velocity vector.

The sum of two null vectors is a null vector. And since a direction is not relevant for a null vector, the resultant has no direction either.

Related questions

there are two simple methods to add vector. 1. head to tail rule. 2.by rectangular component method.

Ion Know ... You Tell Me

Consider an equilateral triangle. If each vector started at the center of the triangle and went through a different vertex than the other two vectors then they would cancel. I believe in order for them to add to a null vector they must be co-planer.

No. The vector resultant of addition of vectors is the vector that would connect the tail of the first vector to the head of the last. For any set of vectors to add to the zero vector, the endpoint of the last vector added must be coincident with the start point of the first. Therefore for the sum of only two vectors to have a chance of being the zero vector, the second vector must be in a direction exactly opposite the first. So you can tell that the result of adding the two vectors could only can be zero vector if the two vectors were of two equal magnitude.

You get a third vector.

Yes, two vectors of similar kind can be added. For example we can add a distance vector with another distance vector. But we cannot add distance vector and velocity vector.

The sum of two null vectors is a null vector. And since a direction is not relevant for a null vector, the resultant has no direction either.

A vector has direction, where as a scalar does not. When you add two vectors, it is like you are moving one vector to the end of the other vector, and closing off the triangle with a vector for the third side. That third vector is the addition of the first two vectors. The new vector points in a specific direction, so it cannot be a scalar.

There are two possible answers to this; a) It has no direction b) It points in all directions Answer a is really more true, as the notion of a null vector precludes any notion of a direction, but the correct answer is b.

Mainly because they aren't scalar quantities. A vector in the plane has two components, an x-component and a y-component. If you have the x and y components for each vector, you can add them separately. This is very similar to the addition of scalar quantities; what you can't add directly, of course, is their lengths. Similarly, a vector in space has three components; you can add each of the components separately.

when you add the measurement of two or more vectors together

Yes. You can consider a vector of being made up of a magnitude (size) and a direction. If any of the two changes, it is no longer the same vector. Alternately, you can also consider a vector (in two dimensions, for simplicity) as being made up of an x-component and a y-component. It is not possible to change the angle without changing at least one of the two components.