222 assignment4

# 222 assignment4 - 4 Find the velocity and acceleration...

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Calculus III Assignment 4 Due on Friday October 22 in class 1. (a) Find the vector normal to the plane through the points P (1 , - 1 , 0) , Q (2 , 1 , - 1)and R ( - 1 , 1 , 2) . (b) Find the area of the triangle formed by the above three points. 2. Find the equation of the plane passing through the line of intersection of the two planes x + y = 2 , y - z = 3 and which is perpendicular to the plane 2 x + 3 y + 4 z = 5. 3. Find the unit tangent vector, the principal normal, the curvature and the arc length of the curve over the interval 1 t 2, for the plane curve R = 2 ln t i + ( 1 t + t ) j ) . Find the equation of the circle of curvature when t = 1.
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Unformatted text preview: 4. Find the velocity and acceleration vectors, the speed ds dt , as well as the tangential and normal components of acceleration for the motion described by R = t i + ln t j for t > . 5. For the curve R = ( t-t 3 / 3) ,t 2 ,t + t 3 / 3), ﬁnd (a) the unit tangent and normal vectors T ( t ) and N ( t ) at any point, (b) Now ﬁnd the curvature κ ( t ), (c) Find the binormal B ( t ) and the torsion τ ( t ), (d) Find the length of the arc of the curve cut oﬀ between the planes z = 0 and z = 12. 1...
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