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Which of the following curves have the same projection onto the xy plane?
a) <t, t^2, e^t>
b) <e^t, t^2, t>
c) <t, t^2, cost>
a) <t, t^2, e^t>
b) <e^t, t^2, t>
c) <t, t^2, cost>
A vector projection is a method of representing a vector onto another vector or onto a plane. It helps to understand the component of a vector in a particular direction.
The vector projection is calculated by finding the dot product of the two vectors and dividing it by the magnitude of the vector onto which the projection is being made. This gives the magnitude of the projected vector. To find the direction, the projection vector is multiplied by the unit vector of the vector onto which the projection is being made.
A vector projection gives both the magnitude and direction of the projected vector, while a scalar projection only gives the magnitude. Vector projection is represented by a vector, while scalar projection is represented by a scalar value.
Vector projection is used in various fields such as physics, engineering, and computer graphics. It is used to calculate the forces acting on an object, determine the components of a vector in a particular direction, and create 3D graphics by projecting 3D objects onto a 2D plane.
Yes, vector projection can be negative. This happens when the angle between the two vectors is greater than 90 degrees. In this case, the projected vector is in the opposite direction of the vector onto which the projection is being made.