A positive scalar multiplied by a vector, will only change the vector's magnitude, not the direction. A negative scalar multiplied by the vector will reverse the direction by 180°.
The answer depends on the context, but bi is a variable, not a number. It could be the ith of a set of variables b1, b2, ... .Or it could be the square root of -b2.Or it could be a vector of magnitude b in the idirection.
raster
Raster images are defined in pixels. ie At every x,y location, whether it is black or white. Vector images are defined by lines. eg From x,y to X,Y. Any pixel that lies between these points on a white background becomes black. It is easier to convert Vector images to Raster images, rather than the other way. Vector images are sometimes smaller (in data size). eg If the image contains one line, then the amount of data needed to store this is smaller than having to define every pixel in the image regardless of whether it is relevant. Vector images can be scaled smaller and larger without any significant loss of detail. Raster images that have been made smaller lose clarity and cannot then be made larger to improve the quality.
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A positive scalar multiplied by a vector, will only change the vector's magnitude, not the direction. A negative scalar multiplied by the vector will reverse the direction by 180°.
When a vector is multiplied by a negative number, it changes direction by 180 degrees but keeps the same magnitude. Therefore, a vector initially acting at 90 degrees would end up acting at 270 degrees (or -90 degrees) after being multiplied by a negative number.
A negative vector is a vector that has the opposite direction of the original vector but the same magnitude. It is obtained by multiplying the original vector by -1. In other words, if the original vector points in a certain direction, the negative vector points in the exact opposite direction.
A vector has a direction associated with it. A number (or scalar) does not.
A null vector has no magnitude, a negative vector does have a magnitude but it is in the direction opposite to that of the reference vector.
Yes, a scalar can be a negative number. For instance: c<x₁,x₂> = <cx₁,cx₂> such that <x₁,x₂> is a vector. Let c = -1 for instance. Then, we have this vector: <-x₁,-x₂> Compared to <x₁,x₂>, <-x₁,-x₂> has negative signs. In physics and mathematics, if we multiply the vector or something by a negative value scalar, then the direction of the vector is reversed, and the magnitude stays the same. If the magnitude increases/decreases, and the direction of the vector is reversed, then we can multiply the vector by any negative non-1 scalar value.
Vectors have magnitude and direction. The magnitude is always a positive number.
In physics, a negative vector is a vector that points in the opposite direction to a positive vector of the same magnitude. Negative vectors are used to represent quantities or forces that act in the opposite direction within a specific coordinate system.
An object can have negative momentum if it is moving in the opposite direction to a chosen positive direction. Momentum is a vector quantity that considers both the mass and velocity of an object, so moving in the opposite direction as chosen positive direction can result in negative momentum.
No, the value can't be negative because magnitude of a vector is just how long it is regardless of its direction. :-)
You should express a vector along the x-axis as negative when it points in the negative x-direction relative to a chosen positive direction. This convention helps maintain consistency with vector addition and trigonometric methods.
It will be twice as large as the original and have the opposite direction.