Vectors are used whenever there is a measurement in which not only the magnitude is relevant, but also the direction. Typical uses of vectors include position, velocity, acceleration, force, torque, and others.
The Resultant Vector minus the other vector
We get the Unit Vector
If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
The normal vector to the surface is a radius at the point of interest.
R3 is a complete vector room, so you can actually take *ANY* other vector, e.g. from r1, r2 or r4 or any other vector room.
The Resultant Vector minus the other vector
We get the Unit Vector
Divide the vector by it's length (magnitude).
If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
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.
find the vector<1,1>+<4,-3>
The normal vector to the surface is a radius at the point of interest.
1) The position vector of a particle is r= (a cosώt) i+ (a sinώt) j. The velocity of the particle is and find the parallel position vector.
R3 is a complete vector room, so you can actually take *ANY* other vector, e.g. from r1, r2 or r4 or any other vector room.
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 magnitude of a vector can be found by taking the square root of each of the vector components squared. For example, if you had the vector 3i+4j, to find the magnitude, you take sqrt ( 3²+4² ) To get: sqrt ( 9+16 ) sqrt ( 25 ) = 5 Works the same in 3D or more, just put all the vector components in.
Given a vector, speed is the magnitude of the velocity vector, |v|. Consider vector V= IVx + JVy + KVz the magnitude is |V| = ( Vx2 + Vy2 + Vz2)1/2