- #1

- 31

- 1

## Homework Statement

A proton moves with a speed ##v = 3 \cdot 10^5 \frac{m}{s}## in the parallel direction to ##i+k##. A magnetic field of ##1T##, in the ##i+j+k## acts over it. Which electric field must we apply in this region so that the Lorentz force over the proton is null?

## Homework Equations

##F = q(\vec{E} + \vec{v}\times\vec{B})##

## The Attempt at a Solution

My first step (and the wrong one) was consider ##\vec{v} = 3\cdot10^5 (i+k)##, then I made the vectorial product ##\vec{v}\times\vec{B}## finding ##3\cdot10^5(-i+k)##, then I simply wanted to find the electric field vector such as ##\vec{E} + 3\cdot 10^5 (-i+k) = \vec{0} \rightarrow \vec{E} = 3\cdot 10^5(i-k)##

My doubt is: how do I represent the velocity vector in this case by knowing its size and which vector it is parallel to?