Find a vector valued function which gives the curve of intersection of y2 + z2 =16 with the plane 2x+z=-11. (The goal is to parametrize x=x(t), y = y(t), z=z(t) as a function of t, and form a function like r_>(t) = x(t), y(t), z(t)>) The Proffessor then says "The equation y2 + z2 =16 tells us to take y= y(t)= 4 cost(t) z= z(t) = 4 sin(t)" I don't understand how he got y= y(t)= 4 cost(t) z= z(t) = 4 sin(t). Please explain in detail.
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.
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The Proffessor then says "The equation y2 + z2 =16 tells us to take
y= y(t)= 4 cost(t)
z= z(t) = 4 sin(t)"
I don't understand how he got
y= y(t)= 4 cost(t)
z= z(t) = 4 sin(t). Please explain in detail.
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