Consider the function F(x,y,z) = x2 – yz + z2 and the point P(−3,5,−1). Find the direction (this doesn’t need to be a unit vector) in which F increases most rapidly at the point P. Compute the maximum rate of change for F at P. The level surface of F which passes through P is S : x2 − yz + z2 = 15. Find an equation in standard form for the tangent plane to S at P. Find a set of parametric equations for the line normal to S at P.
Consider the function F(x,y,z) = x2 – yz + z2 and the point P(−3,5,−1). Find the direction (this doesn’t need to be a unit vector) in which F increases most rapidly at the point P. Compute the maximum rate of change for F at P. The level surface of F which passes through P is S : x2 − yz + z2 = 15. Find an equation in standard form for the tangent plane to S at P. Find a set of parametric equations for the line normal to S at P.
Consider the function F(x,y,z) = x2 – yz + z2 and the point P(−3,5,−1). Find the direction (this doesn’t need to be a unit vector) in which F increases most rapidly at the point P. Compute the maximum rate of change for F at P. The level surface of F which passes through P is S : x2 − yz + z2 = 15. Find an equation in standard form for the tangent plane to S at P. Find a set of parametric equations for the line normal to S at P.
Consider the function F(x,y,z) = x2 – yz + z2 and the point P(−3,5,−1).
Find the direction (this doesn’t need to be a unit vector) in which F increases most rapidly at the point P.
Compute the maximum rate of change for F at P.
The level surface of F which passes through P is S : x2 − yz + z2 = 15. Find an equation in standard form for the tangent plane to S at P.
Find a set of parametric equations for the line normal to S at P.
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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