Q: Can a vector have zero component along a line and still have non-zero magnitude?

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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.

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.

Vector b would be along the z axis, it could have any magnitude.

Their directions are perpendicular.

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.

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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.

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.

The three parts of a vector quantity are magnitude, direction, and orientation. Magnitude refers to the size or length of the vector, direction indicates the line along which the vector acts, and orientation specifies the starting point of the vector.

At what angle should a vector be directed to so that its x component is equal to its y component

No, a vector directed along the y-axis does not have an x component. A vector along the y-axis only has a component in the y direction.

Vector b would be along the z axis, it could have any 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.

The tangential component of acceleration is the change in speed along the direction of motion, while the normal component is the change in direction of velocity. In other words, tangential acceleration affects the speed of an object, while normal acceleration affects the direction of motion.

No, the magnitude of a vector cannot be greater than the sum of its components. The magnitude of a vector is always equal to or less than the sum of the magnitudes of its components. This is known as the triangle inequality.

Resolving a vector into components means breaking down the vector into perpendicular vectors that align along the coordinate axes. For example, a vector of magnitude 10 at an angle of 30 degrees with the x-axis can be resolved into x-component = 10cos(30) and y-component = 10sin(30) where cos(30) = √3/2 and sin(30) = 1/2.

In vector terms, a component refers to the portion of the vector along a particular direction or axis. It is the projection of the vector onto that specific direction. For example, a vector in two dimensions can be broken down into its horizontal and vertical components.

Their directions are perpendicular.