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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 else can I help you with?
What are vector components?
prrpendicular projections of a vector called component of vector
Define the unit vector?
The unit vector is a vector whose magnitude is 1.
How do you find the component of a vector perpendicular to another vector?
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
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
What is null vector?
NULL VECTOR::::null vector is avector of zero magnitude and arbitrary direction the sum of a vector and its negative vector is a null vector...
Can a vector have positive and negative components?
Yes, a vector can have both positive and negative components. In a two-dimensional space, for example, a vector can point in a direction where one component (such as the x-component) is positive while the other component (the y-component) is negative. This allows the vector to represent a direction that combines movement in different quadrants of the coordinate system. Thus, vectors can effectively capture a wide range of directional information.
Dot product of unit vectors of cartesian and cylindrical coordinate system?
Unit vectors are perpendicular. Their dot product is zero. That means that no unit vector has any component that is parallel to another unit vector.
What is a projection of a vector along an axis of a coordinate system called?
The projection of a vector along an axis of a coordinate system is called a "component" of the vector. For a given vector, its component along a specific axis is determined by taking the dot product of the vector with a unit vector in the direction of that axis. This process effectively measures how much of the vector aligns with that axis. Each axis in the coordinate system has its own corresponding component of the vector.
Can a vector have a component greater than the magnitude of vector?
no a vector cannot have a component greater than the magnitude of vector
Will a vector be zero if anyone of its component is zero?
If any component of a vector is not zero, then the vector is not zero.
Can a vector have a component greater than the vector's magnitude?
No, a vector's component cannot be greater than the vector's magnitude. The magnitude represents the maximum possible magnitude of a component in any direction.
Vector component greater than the vectors magnitude?
can a vector have a component greater than the vector magnitude
Can a vector be represented in terms of unit vector?
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
Is the vector (I j k) a unit vector?
No, the vector (I j k) is not a unit vector. In the context of unit vectors, a unit vector has a magnitude of 1. The vector (I j k) does not have a magnitude of 1.
Can a vector have a component greater than the magnitude of the vector?
No, a vector component is a projection of the vector onto a specific direction. It cannot have a magnitude greater than the magnitude of the vector itself.
What are vector components?
prrpendicular projections of a vector called component of vector
What is the difference between a unit vector and a unit basis vector?
A unit vector is a vector with a magnitude of 1, while a unit basis vector is a vector that is part of a set of vectors that form a basis for a vector space and has a magnitude of 1.
