Suppose the magnitude of the vector is V and its direction makes an angle A with the x-axis, then
the x component is V*Cos(A)
and the y component is V*Sin(A)
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
All Components cancel The Component vector sum is zero Example: x-components A<------------------->B = zero same for y-components
It depends on the vector!
At what angle should a vector be directed to so that its x component is equal to its y component
In 2 dimensions the angle made by the displacement vector with the positive x-axis is arctan(y/x).
If you assume the vector is only in two dimensions, you can find the missing y-component with Pythagoras' Theorem: y = square root of (magnitude2 - x2).
Given the vector in angle-radius form? y-component=r sin(theta), x-component=r cos(theta)
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
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.
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
The sum of any number of vectors is itself a vector, just as the sum of any number of scalars (normal numbers) is a normal number.If a vector is resolved into 2 components, x and y, in the form [x,y], then it can be added to any other vector resolved into 2 components [z,a].[x,y]+[z,a]=[x+z,y+a]
Read the theory part of your book before you ask these questions
You must find the x and y components of each vector. Then you add up the like x components and the like y components. Using your total x component and total y component you may then apply the pythagorean theorem.
You don't. Knowing two of the vector's orthogonal components doesn't tell you what the third one is. It could be absolutely anything.
A vector can be represented in terms of its rectangular components for example : V= Ix + Jy + Kz I, J and K are the rectangular vector direction components and x, y and z are the scalar measures along the components.
Velocity is a vector, you can sum velocity in terms of direction components such as x and y.
Any vector could be resolved into perpendicular components one along x axis and the other along y axis. So all vectors would be split into two components. Now we can easily add the x components and y components. If all in the same simply addition. If some are in opposite we have to change its sign and add them. Finally we will have only two one along x and another along y. Now we can get the effective by using Pythagoras.