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Can a vector have zero component along a line and still have non-zero magnitude?
Aimsunique
Yes, if it has a non-zero component along some other line - usually, but not necessarily orthogonal.
Wiki User
∙ 13y ago
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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.
Can the magnitude of a vector be lesser than its component?
No, because the components along any other direction is v*cos(A) where v is the magnitude of the original vector and A is the angle between the direction of the original vector and the direction of the component. Since the absolute value of cos(A) cannot be greater than 1, then v*cos(A) cannot be greater than v.
A vector a is along the positive z axis and it's vector product with another vector b is zero then vector b could be?
Vector b would be along the z axis, it could have any magnitude.
If the component of vector A along the direction of vector B is zero. What can you conclude about these two vectors?
Their directions are perpendicular.
What is the maximum value a 5 N vector and an 8 N vector can have?
Acting simultaneously along the same line and in the same direction, they have the same effect as a single vector in that direction with a magnitude of 13 N.
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.
Can the magnitude of a vector be lesser than its component?
No, because the components along any other direction is v*cos(A) where v is the magnitude of the original vector and A is the angle between the direction of the original vector and the direction of the component. Since the absolute value of cos(A) cannot be greater than 1, then v*cos(A) cannot be greater than v.
Can a vector directed along x-axis have y-axis component?
At what angle should a vector be directed to so that its x component is equal to its y component
Can a magnitude of vector greater than its components?
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 a is along the positive z axis and it's vector product with another vector b is zero then vector b could be?
Vector b would be along the z axis, it could have any magnitude.
The figure shows two vector B and C along with magnitude and direction . D is given by D =B -C. What is the magnitude of vector of D What angle does vector D make with the +x-axis?
Nothing
If the component of vector A along the direction of vector B is zero. What can you conclude about these two vectors?
Their directions are perpendicular.
If one component of a vector A is zero along the direction of another vector B then in what direction the two vectors will be?
opposite direction.
Why is speed classified as a scalar quantity and velocity classified as a vector quantity?
Speed is the rate of which an object is moving altogether and is a scalar quantity and thus only requires a magnitude and is found by the use of the formula speed=distance/time SI unit = m.s-1 Velocity is the rate of which a object is moving in a given direction, so is vector quantity and both a magnitude and direction are required found by the formula velocity=displacement/time SI unit = m.s-2
Can a vector with a non zero component be zero?
No. The answer does assume that "components" are defined in the usual sense - that is, a decomposition of the vector along a set of orthogonal axes.
What does vector mean in science terms?
Any physical quantity which has both direction and magnitude is called a vector. A quantity must also obey the 'Triangle law of vector addition' to be called as a vector. For example displacement is a vector, u can say a person moved 5 km (magnitude) along west(direction). But electric current is not a vector, it has magnitude and its direction is from +ve terminal to -ve terminal but it doesn't obey triangle law. Rather currents are added as scalars.
What is the maximum value a 5 N vector and an 8 N vector can have?
Acting simultaneously along the same line and in the same direction, they have the same effect as a single vector in that direction with a magnitude of 13 N.
