Find the vector and parametric equations for the line through the point P(1,1,3) and parallel to the vector -2i + 1j + 2k 1. Vector Form r=(<_,_,3>)+t(<_,_,2>) 2. Parametric form (parameter t, and passing through P when t=0): x=x(t)= y=y(t)= z=z(t)=
Vector Arithmetic
Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
Find the
1. Vector Form r=(<_,_,3>)+t(<_,_,2>)
2. Parametric form (parameter t, and passing through P when t=0):
x=x(t)=
y=y(t)=
z=z(t)=
Given:
P=(1,1,3)=(x0, y0, z0)
v=-2i+j+2k=<-2,1,2>=<a, b ,c>
Explanation:
1] Vector equation of a line can given by,
r=<x ,y ,z>
r0=<x0, y0, z0>
r=r0+t<v1, v2 ,v3>
Therefore,
r=<1,1,3>+t<-2,1,2>
This is the required vector form of the line.
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