Question

Let u = <-3, 4>, v = <8, 2>. Find u + v.

help me please

Answer 1

Answer on Question #42440 – Math - Analytic Geometry

Let $\mathbf{u} = (-3,4), \mathbf{v} = (8,2)$.

Find $\mathbf{u} + \mathbf{v}$.

Given two vectors $\mathbf{u} = (u_{1}, u_{2})$ and $\mathbf{v} = (v_{1}, v_{2})$ in the Euclidean plane, the sum is given by:

$$\overline{\mathbf{u} + \mathbf{v}} = (u_{1} + v_{1}, u_{2} + v_{2})$$

In other words, vector addition is just like ordinary addition: component by component.

Notice that if you add together two 2-dimensional vectors you must get another 2-dimensional vector as your answer. Addition of 3-dimensional vectors will yield 3-dimensional answers. 2- and 3-dimensional vectors belong to different vector spaces and cannot be added. These same rules apply when we are dealing with scalar multiplication.

Thus,

$$\overline{\mathbf{u} + \mathbf{v}} = (-3 + 8, 4 + 2)$$ $$\overline{\mathbf{u} + \mathbf{v}} = (5,6)$$

Answer: $\overline{\mathbf{u} + \mathbf{v}} = (5,6)$