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.
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.
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.
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.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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