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What is a projection of a vector along an axis of a coordinate system called?
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What are the two vectors projected on the axes of a coordinate system?
If you have a vector of magnitude r, making an angle of a degrees, then its projection on the x-axis is r*cos(a) and on the y-axis it is r*sin(a).
How do you find the direction of the vector?
I suspect the question arises from confusion. A vector itself already defines a direction, usually in the Cartesian xyz coordinate system. If you want to express the direction in other coordinates, such as polar or spherical coordinates you need to transform the vector to these coordinate systems. I can answer you question more fully if you can specify the specific coordinate system in which you want to know the direction.
When will be the vector projection and vector components are same?
Ans :The Projections Of A Vector And Vector Components Can Be Equal If And Only If The Axes Are Perpendicular .
If you have selected a coordinate system you can express a two-dimensional vector using a pair of quantities known collectivelly as?
Components.
Ten vectors addtogether to give zero resultant it is possible that nine of this vectors are in the same plane but the tenth not on this plane?
No. Let's assume the plane has coordinates x and y; the vector outside the plane has a component for the z-coordinate. In that case, another vector (or several) must also have a component in the z-coordinate, to compensate.No. Let's assume the plane has coordinates x and y; the vector outside the plane has a component for the z-coordinate. In that case, another vector (or several) must also have a component in the z-coordinate, to compensate.No. Let's assume the plane has coordinates x and y; the vector outside the plane has a component for the z-coordinate. In that case, another vector (or several) must also have a component in the z-coordinate, to compensate.No. Let's assume the plane has coordinates x and y; the vector outside the plane has a component for the z-coordinate. In that case, another vector (or several) must also have a component in the z-coordinate, to compensate.
What are the projections of a vector along the axes of a coordinate system?
A tangent of the vector is the projection of a vector along the axes of a coordinate system.
The components of a vector will be the same no matter what coordinate system is used to express that vector?
Yes, that is correct. The components of a vector, which represent its magnitude and direction in a particular coordinate system, are independent of the choice of coordinate system used to express the vector. This property is a fundamental characteristic of vectors in mathematics and physics.
What are the two vectors projected on the axes of a coordinate system?
If you have a vector of magnitude r, making an angle of a degrees, then its projection on the x-axis is r*cos(a) and on the y-axis it is r*sin(a).
Is there only one unique coordinate system in which vector components can be added?
No, there are multiple coordinate systems in which vector components can be added, such as Cartesian, polar, and spherical coordinates. The choice of coordinate system depends on the problem at hand and the geometry of the situation being analyzed.
How do you find the direction of the vector?
I suspect the question arises from confusion. A vector itself already defines a direction, usually in the Cartesian xyz coordinate system. If you want to express the direction in other coordinates, such as polar or spherical coordinates you need to transform the vector to these coordinate systems. I can answer you question more fully if you can specify the specific coordinate system in which you want to know the direction.
What is the direction of zero vector?
The zero vector has no direction because it has a magnitude of zero. It is represented by a point at the origin in a coordinate system, with no specific direction.
What number is the length of a vector?
The length of a vector is a scalar quantity, typically denoted as a positive real number, that represents the magnitude or size of the vector. It is calculated using the vector's components in a coordinate system, often with the Pythagorean theorem.
When will be the vector projection and vector components are same?
Ans :The Projections Of A Vector And Vector Components Can Be Equal If And Only If The Axes Are Perpendicular .
What is necessary in order to show the correct direction of a vector?
To show the correct direction of a vector, you need to specify the reference point or origin from which the vector is being measured, and also indicate the angle or orientation at which the vector is pointing relative to that reference point. This information can be represented using coordinate axes, angles, or directional headings.
What does the length of a position vector represent?
The length of a position vector represents the distance of the point it is referencing from the origin in the coordinate system. It is also known as the magnitude of the vector.
If you have selected a coordinate system you can express a two-dimensional vector using a pair of quantities known collectivelly as?
Components.
These give direction to a force vector?
The components of a force vector describe the magnitude and direction of the force in a specific coordinate system. The angle of the force vector is also important in determining its direction relative to the coordinate axes. Additionally, the sign conventions for the components indicate the orientation of the force along each axis.
