Question

a force 10N is in x direction . Represent it in vactor form​

Answer 1

Answer:

Everyone has given the “sin = opp/hyp” answer (aside from Victor Avasi who suggests scale drawings - a great idea!) Anyway, I thought I’d offer a different way of thinking about it. When decomposing a vector ∣∣V⃗ ∣∣=V , we always have that one of the legs is Vs=Vsin(θ) and one is Vc=Vcos(θ) . Note that I’m avoiding using subscripts x & y here because the legs needn’t be parallel to the x & y axes - you are welcome to decompose a vector into any coordinate system.

For complex cases the angle that you aren’t given might not even be “in the triangle” of the vector that you are decomposing and its legs, which can make the problem hard to solve geometrically. But, if you know that sin(θ)→0 as θ→0 then you can reason without doing geometry. For example, in your case the angle is with the y-axis. If that angle were to shrink (head towards zero) then the length that you are interested in, the x-component, would also shrink. That means that the x-component (in this case) is Vsin(θ) . Note that if the angle were instead with the x-axis, that if the angle were to go to zero then the x-component would actually grow. That is the behavior of cosine, so in that case we'd have Vx=Vcos(θ).