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If all the components of a vector are equal to 1 then that vector is a unit vector?
Wiki User
∙ 11y ago
False.
Wiki User
∙ 11y ago
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Can the magnitude of a vector be equal to one of its components?
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.
How would you define the zero vector by using the idea of components?
All components of the zero vector equal to zero.
How do vector components compare in size to the vector from which they came?
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
Can a vector have a zero magnitude if all of its components are zero?
If all the components of a vector are zero, the magnitude of the vector will always be zero.
Can the magnitude of a vector be ever equal to one of its components?
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.
Can the magnitude of a vector be equal to one of its components?
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.
How would you define the zero vector by using the idea of components?
All components of the zero vector equal to zero.
How do vector components compare in size to the vector from which they came?
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
Can a vector have a zero magnitude if all of its components are zero?
If all the components of a vector are zero, the magnitude of the vector will always be zero.
Can the magnitude of a vector be ever equal to one of its components?
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.
What will happen if all components of a vector are reversed in direction?
Then the resultant vector is reversed.
Can a vector have a component equal to zero and still have a nonzero magnitude?
Yes. For instance, the 2-dimensional vector (1,0) has length sqrt(1+0) = 1 A vector only has zero magnitude when all its components are 0.
Will a vector be zero if one of its compoent is zero?
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.
What items must be stated to specify to a vector quantity completely?
The vector magnitude and direction or the components of the vector.
A vector may be resolved into only two components?
No, a vector in 3-d space would normally be resolved into 3 components. It all depends on the dimensionality of the space that you are working within.
What is equalibrium in physics?
The sum of all forces is equal to zero when added using the vector method The sum of all torque is equal to zero when added using the vector method
How do you find the magnitude of a vector?
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.
