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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.
Can a vector have zero magnitude if one of its components is nonzero?
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
Can a vector have 0 component along a line and still have non zero magnitude?
Huh?I have been kicking around your question in my mind for five minutes trying to figure out an answer or a way to edit your question into an unambiguous form, but I'm stumped. I don't know what you mean by "zero component along a line."If you look at the representation of a vector on paper using a Cartesian coordinate system -- in other words, one using x and y axes -- the orthogonal components of the vector are the projections of the vector on the x and y axes. If the vector is parallel to one of the axes, its projection on the other axis will be zero. But the vector will still have a non-zero magnitude. Its entire magnitude will project on only one axis.But a vector must have magnitude AND direction. And if it has zero magnitude, its direction cannot be determined.Still trying to make heads or tails out of your question.......If you draw a random vector on a Cartesian grid, it will have an x component and a y component, which are both projections of the original vector upon the axes. However, it could also be represented by projecting it onto a new set of orthogonal axes -- call them x' and y' -- where the x' axis is oriented to be parallel to the original vector and the y' vector is perpendicular to it. In that case, the x' component will have a magnitude equal to the magnitude of the original vector -- in other words, a non-zero value along a line parallel to the x' axis -- and a zero magnitude in the y' direction.
What can you say about two vectors if vector A vector B 0?
Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
Can a component of a vector be greater than the vector's magnitude?
No. If the vector is 2D then it's magnitude is (x^2+y^2)^0.5 where x and y are the components and ^0.5 means take the square root. In 3D this becomes (x^2+y^2+z^2)^0.5 etc. Thus the magnitude is always at least as big as one of the components. Here's an example of a 3D vector: (3,4,5) |(3,4,5)|=(3^2+4^2+5^2)^0.5=(9+16+25)^0.5=50^0.5=7.07... If y and z were 0: (3,0,0) |(3,0,0)|=(3^2+0^2+0^2)^0.5=(9+0+0)^0.5=9^0.5=3 ie the magnitude is the same size as x. You can also consider this geometrically. A vector is an arrow and the magnitude represents the length of the arrow. Vector addition is the 'adding' of these arrows so (3,4,5)=(3,0,0)+(0,4,0)+(0,0,5). Clearly the length of an arrow built of three smaller ones can't be less than any one of them.
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.
Can a vector have zero magnitude if one of its components is nonzero?
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
What is the magnitude of vector -2 0?
A vector, starting at the origin and going to point (-2,0):Since there is no y-component, the magnitude is the absolute value of the x componentmagnitude = 2magnitude of a vector = sqrt( X2 + Y2) = sqrt ((-2)2 + 02) = sqrt(4) = 2where X & Y are the x-component & y-component of the vector.
Suppose vector equation A plus B equals 0.how does the magnitude of B compare to that of A?
If vector equation A + B = 0, it means that vector B is equal in magnitude but opposite in direction to vector A. Therefore, the magnitude of vector B is equal to the magnitude of vector A.
When do you get a magnitude of 0 in vector?
The magnitude of a vector is 0 if the magnitude is given to be 0.The magnitude of the resultant of several vectors in n-dimensional space is 0 if and only if the components of the vectors sum to 0 in each of a sewt of n orthogonal directions.
Which vector have no magnitude?
The zero vector has no magnitude. v= Io + Jo + k0 has no magnirude |V|= sqroot(o^2 + 0^2 + 0^2)=0.
Why null vector has a direction as it has magnitude 0?
The null vector is a special case where both magnitude and direction are undefined. This vector represents a point in space, rather than a physical quantity with magnitude and direction.
Can a vector have 0 component along a line and still have non zero magnitude?
Huh?I have been kicking around your question in my mind for five minutes trying to figure out an answer or a way to edit your question into an unambiguous form, but I'm stumped. I don't know what you mean by "zero component along a line."If you look at the representation of a vector on paper using a Cartesian coordinate system -- in other words, one using x and y axes -- the orthogonal components of the vector are the projections of the vector on the x and y axes. If the vector is parallel to one of the axes, its projection on the other axis will be zero. But the vector will still have a non-zero magnitude. Its entire magnitude will project on only one axis.But a vector must have magnitude AND direction. And if it has zero magnitude, its direction cannot be determined.Still trying to make heads or tails out of your question.......If you draw a random vector on a Cartesian grid, it will have an x component and a y component, which are both projections of the original vector upon the axes. However, it could also be represented by projecting it onto a new set of orthogonal axes -- call them x' and y' -- where the x' axis is oriented to be parallel to the original vector and the y' vector is perpendicular to it. In that case, the x' component will have a magnitude equal to the magnitude of the original vector -- in other words, a non-zero value along a line parallel to the x' axis -- and a zero magnitude in the y' direction.
What can you say about two vectors if vector A vector B 0?
Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
Can the magnitude if the difference between two vectors ever be greater than the magnitude of their sum?
No, the magnitude of the difference between two vectors cannot be greater than the magnitude of their sum. This is due to the triangle inequality, which states that the magnitude of the sum of two vectors is always greater than or equal to the magnitude of their difference.
How can a null vector be a vector if there is no direction?
A null vector does not have a direction but still satisfies the properties of a vector, namely having magnitude and following vector addition rules. It is often used to represent the absence of displacement or a zero result in a vector operation.
Under what circumstances can a vector have components that are equal in magnitude?
(Magnitude of the vector)2 = sum of the squares of the component magnituides Let's say the components are 'A' and 'B', and the magnitude of the vector is 'C'. Then C2 = A2 + B2 You have said that C = A, so C2 = C2 + B2 B2 = 0 B = 0 The other component is zero.
