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Can a vector have a zero magnitude if all of its components are zero?
Wiki User
∙ 14y ago
If all the components of a vector are zero, the magnitude of the vector will always be zero.
Wiki User
∙ 14y 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.
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.
How would you define the zero vector by using the idea of components?
All components of the zero vector equal to 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.
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.
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.
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.
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.
How would you define the zero vector by using the idea of components?
All components of the zero vector equal to 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 items must be stated to specify to a vector quantity completely?
The vector magnitude and direction or the components of the vector.
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.
Formula to calculate magnitude of the resultant vector?
To calculate the magnitude of the resultant vector, you can use the Pythagorean theorem. Square the x-component of the vector, square the y-component of the vector, and sum them together. Finally, take the square root of the resulting sum. The formula is: |R| = sqrt((Rx^2) + (Ry^2)).
A B 0 what can you say about the components of the two vectors?
One of them is negative or both of them are zero,
Is A plus B equals 0 what can you say about the components of the two vectors?
All Components cancel The Component vector sum is zero Example: x-components A<------------------->B = zero same for y-components
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.:)
Can you find a vector quantity that has a magnitude of zero but components that are different from zero?
No, that's not possible - at least, not with vectors over real numbers. The magnitude of a vector of components a, b, c, d, for example, is the square root of (a2 + b2 + c2 + d2), and as soon as any of those numbers is different from zero, its square, the sum, and the square root of the sum will all be positive. It is not possible (in the real numbers) to compensate this with a negative number, since the square of a real number can only be zero or positive. Another answer: In special relativity we use a metric for vectors different from the Euclidean one mentioned above. If (t, x, y, z) is a 4-vector in Minkowski space the squared "length" is defined as t2 - x2 - y2 - z2. As you can see this can be negative (for spacelike vectors), positive (for timelike vectors) or zero (for null, or lightlike vectors). See related link for more information
