Yes. A vector in two dimensions is broken into two components, a vector in three dimensions broken into three components, etc... If the value of all but one component of a vector equal zero then the magnitude of the vector is equal to the non-zero component.
A vector comprises its components, which are orthogonal. If just one of them has magnitude and direction, then the resultant vector has magnitude and direction. Example:- If A is a vector and Ax is zero and Ay is non-zero then, A=Ax+Ay A=0+Ay A=Ay
The answer below assumes you are required to find the components of the vector. A vector with unity magnitude means that the magnitude of the vector equals to 1. Therefore its a simple case of calculating the values of sin(45) for the vertical components and cos(45) for the horizontal components. Both of these values equal to 1/sqrt(2) {one over square-root two}
Yes. - if all the other components are zero. When the word "component" means the mutually perpendicular vectors that add (through vector addition) to form the resultant, then then answer is that "the magnitude of a vector" can equal one of its components, if and only if all other components have zero length (magnitude). This answer applies to the typical case of a vector being expressed in terms of components defined by an orthogonal basis. In normal space, these basis vectors merely define the relevant orthogonal coordinate system. There are, however, mathematical systems that use a nonorthogonal basis and the answer is different and presumably not part of the submitted question.
a unit vector is a vector which has exact same direction and has its length or magnitude equal to one
No a vector may not have a component greater than its magnitude. When dealing with highschool phyics problems, the magnitude is usually the sum of two or more components and one component will offset the other, causing the magnitude to be less then its component
Unless the vector is one dimensional, or only valued along one base in a multidimensional space, in which case the magnitude is equal to it's components, a vector's magnitude has to be greater than its components.
A vector comprises its components, which are orthogonal. If just one of them has magnitude and direction, then the resultant vector has magnitude and direction. Example:- If A is a vector and Ax is zero and Ay is non-zero then, A=Ax+Ay A=0+Ay A=Ay
No. In order for the magnitude of a vector to be zero, the magnitude of all of its components will need to be zero.This answer ignores velocity and considers only the various N-axis projections of a vector. This is because direction is moot if magnitude is zero.
The answer below assumes you are required to find the components of the vector. A vector with unity magnitude means that the magnitude of the vector equals to 1. Therefore its a simple case of calculating the values of sin(45) for the vertical components and cos(45) for the horizontal components. Both of these values equal to 1/sqrt(2) {one over square-root two}
Yes. - if all the other components are zero. When the word "component" means the mutually perpendicular vectors that add (through vector addition) to form the resultant, then then answer is that "the magnitude of a vector" can equal one of its components, if and only if all other components have zero length (magnitude). This answer applies to the typical case of a vector being expressed in terms of components defined by an orthogonal basis. In normal space, these basis vectors merely define the relevant orthogonal coordinate system. There are, however, mathematical systems that use a nonorthogonal basis and the answer is different and presumably not part of the submitted question.
Only if one of them has a magnitude of zero, so, effectively, no.
a unit vector is a vector which has exact same direction and has its length or magnitude equal to one
No a vector may not have a component greater than its magnitude. When dealing with highschool phyics problems, the magnitude is usually the sum of two or more components and one component will offset the other, causing the magnitude to be less then its component
The magnitude of (i + 2j) is sqrt(5). The magnitude of your new vector is 2. If both vectors are in the same direction, then each component of one vector is in the same ratio to the corresponding component of the other one. The components of the known vector are 1 and 2, and its magnitude is sqrt(5). The magnitude of the new one is 2/sqrt(5) times the magnitude of the old one. So its x-component is 2/sqrt(5) times i, and its y-component is 2/sqrt(5) times 2j. The new vector is [ (2/sqrt(5))i + (4/sqrt(5))j ]. Since the components of both vectors are proportional, they're in the same direction.
Only if one of them has a magnitude of zero, so, effectively, no.
A unit vector has a length (magnitude) equal to 1 (one unit). A rectangular vector is a coordinate vector specified by components that define a rectangle (or rectangular prism in three dimensions, and similar shapes in greater dimensions). The starting point and terminal point of the vector lie at opposite ends of the rectangle (or prism, etc.).
A vector quantity is one that has a magnitude (a number), and a direction. No, resistance is not a vector quantity; it is a scalar quantity (only magnitude).