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Can a vector have 0 component along a line and still have non zero magnitude?
Wiki User
∙ 13y ago
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.
Wiki User
∙ 13y ago
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Can a vector have zero component along a line and still have non-zero magnitude?
Yes, if it has a non-zero component along some other line - usually, but not necessarily orthogonal.
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.
Is their any physical quantity having both magnitude and direction still not a vector?
I don't think so - is something has a magnitude and a direction, by definition it is a vector.
How do you find the y-component of a vector if you are not given the magnitude of the vector?
It depends on what other information you are given. If you are given the x-component and the angle, then you can still use trig by doing the following. Tan(angle)=y/x If you do not have the x component, then you will need to use other kinematic equations to find the answer. The different ways to find this information are too numerous to list out, but I will give an example of a common one. If you are given the horizontal distance and time the object flies, use d=vt to find the x component of velocity, then use the first strategy.
Are two vectors having equal magnitude?
It depends. Magnitude is technically the length of the vector represented by v. our equation of the magnitude is given by: v= SQRT( x^2 + y^2) You can have 2 similar vectors pointing at different directions and still get the same magnitude.
Can a vector have zero component along a line and still have non-zero magnitude?
Yes, if it has a non-zero component along some other line - usually, but not necessarily orthogonal.
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.
Is their any physical quantity having both magnitude and direction still not a vector?
I don't think so - is something has a magnitude and a direction, by definition it is a vector.
Can unit vector have negative component?
Yes, a unit vector can have negative component since a unit vector has same magnitude and direction as a negative unit vector. Here is the general work out of the problem: Let |v| be the norm of (v1, v2). Then, the unit vector is (v1/|v|, v2/|v|). Determine the "modulus" or the norm |(v1/|v|, v2/|v|)| to get 1, which is the new norm. If we determine the norm of |(-v1/|v|, -v2/|v|)|, we still have the same norm 1.
What is it when two vectors' dot product is one?
That fact alone doesn't tell you much about the original two vectors. It only says that (magnitude of vector-#1) times (magnitude of vector-#2) times (cosine of the angle between them) = 1. You still don't know the magnitude of either vector, or the angle between them.
How do you find the y-component of a vector if you are not given the magnitude of the vector?
It depends on what other information you are given. If you are given the x-component and the angle, then you can still use trig by doing the following. Tan(angle)=y/x If you do not have the x component, then you will need to use other kinematic equations to find the answer. The different ways to find this information are too numerous to list out, but I will give an example of a common one. If you are given the horizontal distance and time the object flies, use d=vt to find the x component of velocity, then use the first strategy.
Is the average speed equal to the magnitude of the average velocity justify your answer?
Yes usually and no rarely, velocity is defined as a vector, having both a direction and a magnitude (which is speed in the case of velocity). For instance 100 mph (speed) east (0o) (direction). In this form it is easy to see that the magnitude is 100 mph but mathematically to determine the magnitude of a vector you would divide the vector by its direction. 100 mph 0o / 0o = 100 mph Average speed and average velocity share the same relationship as instantaneous speed and instantaneous velocity so divide out the average direction from your average velocity to determine your average speed. If this is over a time period and you know the beginning and ending places in space your averages will simply be the difference from the starting to the ending places. So yes so long as you define speed to actually be the magnitude of the vector. However, if speed is taken without direction over time it may become something different. If an object travels along a vector with a negative magnitude its speed will not be negative but its vector magnitude will. Ex: A car travelling in reverse still has a positive speed but a compass will show it to be heading in the opposite direction of travel, a negative vector value...
Are two vectors having equal magnitude?
It depends. Magnitude is technically the length of the vector represented by v. our equation of the magnitude is given by: v= SQRT( x^2 + y^2) You can have 2 similar vectors pointing at different directions and still get the same magnitude.
How can an object stay at same speed and still be accelerating?
acceleration is change in velocity over time. It is important to know that speed is not a vector quantity; it is scalar (meaning it does not have direction), -- velocity does. Therefore, speed is only the MAGNITUDE of velocity. Also, acceleration is a vector quantity meaning it has both magnitude and direction. If you change EITHER magnitude or DIRECTION, acceleration changes. Okay anyway to answer your question, You can have the same magnitude of velocity (aka same speed) and still be accelerating if YOU CHANGE DIRECTION. --- gh
Is extension a scalar or vector quantity?
Scalar quantity has only magnitude , but no direction while vector quantity has both magnitude and direction.You can understand it by comparing speed and velocity.Velocity has magnitude of speed in a particular direction (or say displacement/time take) while speed only defines the rate of distance covered (no direction). If you are still unable to get your answer for your question then please, elaborate or give some description of extension. -Ajlan Wasfi Khan
The velocity of an object can what if the speed of an object remains constant?
The velocity can still change, even if the speed doesn't. This is because velocity is a vector - not only the magnitude is important, but also the direction.
Is velocity a vector or a scalar?
no its a vector quantity,not a scalar quantity,bcz still it z a velocity bt NT a speed On a typical journey the average velocity is the straight-line distance between the start and finish, divided by the time taken, and it also has a direction. The average speed is the actual distance run, divided by the speed. The average speed might not be equal to the magnitude of the average velocity. For example on a round trip the average speed might be 40 mph, while the average velocity is zero.
