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Vectors are usually decomposed into their orthogonal components so to derive equations along those orthogonal axes.
For example, consider a ball thrown at an angle to the horizon and assume, for the sake of simplicity, that the only force acting on it is gravity. Then, if you decompose the vector representing the initial velocity into a horizontal and vertical component, the former will not be affected by another force while the latter will be affected by gravitational acceleration. That will give you an equation which will enable you to work out the flight time and therefore the distance that the ball will travel.
The important thing is that vectors at right angles to one another do not interact. So if you can decompose a vector along orthogonal lines, any other vector at right angles to the original, can be ignored.
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If the component of vector A along the direction of vector B is zero. What can you conclude about these two vectors?
Their directions are perpendicular.
Why you are using cosine function in dot product of two vectors?
It comes from the Law of Cosines. * * * * * For any two vectors A and B, the projection of A onto B, that is, the component of A along B, is ab.cos(x) where x is the angle between the two vectors. By symmetry, this is also the projectoin of B onto A.
What is the Smallest magnitude of sum of 4 and 3 meter vectors?
The smallest magnitude resulting from the addition of vectors with individual magnitudes of 4 and 3 is 1, obtained when the directions of the two component vectors are 180 degrees apart.
If A plus B equals 0 what can you say about the components of the two vectors?
The component vector sum is zero and the all components cancel out.:)
What is the difference between a resultant vector and a component vector?
Oh, dude, okay, so like, a resultant vector is the overall effect of two or more vectors combined, while a component vector is just one of the vectors that make up the resultant. It's like saying the whole pizza is the resultant, and the pepperoni and cheese slices are the component vectors. So, basically, the resultant is the big picture, and the components are just the pieces that make it up.
