The unit vector along r(t) will be 3t–4t^2+2
A vector is a quantity with direction and magnitude that is especially useful for locating one location in space in relation to another. A quantity or phenomena with independent qualities for both size and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields weight are a few examples of vectors in nature.
Given the the position of particle as a function of particle of time is given by: r(t)=3tî–4t^2j+2k. Where î & j are unit vector along the x-axis and y-axis respectively.
We have to find the unit vector along r(t)
To find the unit vector along r(t) we have to put the value of (i,j,k) = (1,1,1) in r(t)
So,
r(t) = 3tî–4t^2j+2k
r(t) = 3t(1)–4t^2(1)+2(1)
r(t) = 3t–4t^2+2
Therefore the unit vector along r(t) will be 3t–4t^2+2
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