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Q: at the origin.
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Please find the normal vector, arc length function s(t) on [0,t], curvature K(t) and radius of curvature p(t)
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- Let vectors A⃗=(2,−4) A → = ( 2 , − 4 ) and B⃗=(−3,1) B → = ( − 3 , 1 ) . Calculate the following: What is the angle θAB θ A B between A⃗ A → and B⃗ B → ?Which of the following statements are correct? Adding two vectors creates a new "resultant" vector. When adding parallel vectors, the resultant vector is the sum of the magnitudes of the original vectors. When adding perpendicular vectors, the resultant vector is the sum of the magnitudes of the original vectors. Graphing calculators always report angles in degrees. Vectors pointing in different direction cannot be subtracted. A vector can be broken into x and y component vectors that sum to equal the original vector. Multiplying a vector by a scalar changes the vector's magnitude and direction.Give a vector parametric equation for the line through the point (5, 3,0) that is parallel to the line (-3 – 4t, 5t – 2, 5 – 4t): L(t) = (Enter your answer as )
- Using spherical polar coordinates r, 0, p to find CM of a uniform solid hemisphere of radius R, whose flat face lies in the xy plane with its center at the origin. The element of volume is in spherical polars of dV = r² dr sine de dip.Jungle gym, dot products, unit vectors. A coordinate system is laid out along the bars of a large 3D jungle gym (the figure below). You start at the origin and then move according to the following steps. For each step, the distance (in meters) and direction in which you move A. are given by the cross product A x B of the given vectors A and B. For example, the first move is 18 m in the +z direction. What is the magnitude dnet of your final displacement from the origin? (a) A = 3.01, B = 6.0 (b) A = - 4.01, B = 3.0k - (c) A = 2.0₁, B = 4.0k (d) A = 3.0₁, B - 8.0 (e) A = 4.0K, B = - 2.01 (f) A = 2.01, B - 4.01Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2). Answer: r(t) =