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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?
B could be either greater than, lesser than or equal to A. 7 +(-7) = 0 (-7) = 7 = 0 0 + 0 = 0
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.
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.
Can the magnitude if the difference between two vectors ever be greater than the magnitude of their sum?
yes,if the components are making angle 0<=theta<=90 no ,the magnitude of vector can never attain a negative value |a|=square root of both components which always gives a positive value
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.
