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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.:)
How resolution of vector is used in applying the component methods in adding vectors?
The related question has a nice detail of this. Each vector is resolved into component vectors. For 2-dimensions, it is an x-component and a y-component. Then the respective components are added. These added components make up the resultant vector.
What is a Resultant Vectors?
resultant vector is a vector which will have the same effect as the sum of all the component vectors taken together.
Two classes of vector?
This question is unfortunately not specific enough. Depending on your criteria you can arbitrarily divide vectors into two (or more) classes. For example I can divide all vectors into those with length 1 and those of other lengths.
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.
How you can add the vectors?
1) Graphically. Move one of the vectors (without rotating it) so that its tail coincides with the head of the other vector. 2) Analytically (mathematically), by adding components. For example, in two dimensions, separate each vector into an x-component and a y-component, and add the components of the different vectors.
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.
How may the resultant of two vectors be computed analytically from vector parallelogram?
To compute the sum (resultant) of two vectors analytically, you divide each vector into components - for example, horizontal and vertical parts (that should add up to the original vector). This can be done with some simple trigonometry. Then, the x-component and y-component (and z-component, if it is in three dimensions) are added separately for the resulting vector.
What is the Formula For Calculating The Magnitude Of The Resultant Of Two Or More Vectors Acting At obtuse Angle?
No matter what the angles are:* Express the vectors in Cartesian (rectangular) coordinates; in two dimensions, this would usually mean separating them into an x-component and a y-component. * Add the components of all the vectors. For example, the x-component of the resultant vector will be the sum of the x-components of all the other vectors. * If you so wish (or the teacher so wishes!), convert the resulting vector back into polar coordinates (i.e., distance and direction).
Do component vectors apply to displacement?
Component vectors can be used with a variety of different used in physics, including displacement, force, acceleration, electric field, etc.
How do you find sum of both vector?
Two methods can be used for vector addition. (1) Graphically. Place the vectors head-to-tail, without changing their direction or size. (2) Analytically, that is, mathematically. Add the x-component and the y-component separately. The z-component too, if the vectors are in three dimensions.
How do you find the component of a vector perpendicular to another vector?
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.
Can a vector have a component greater than vectors magnitude?
No.
