




Suppose a plane passes through the points O(0,0,0). B(1,2,2) and C(-1,-1,2) and u -OB and v-OC. (See figure below.) The vector equation of the plane is:x-sutv Choose... s=0, t=0 s-1, t-1 (5,8,2) s--3...
A particle starts from rest at (0,0,0) at t=0 with velocity vector V=(3t2i-4tj+2t3k)m/s. 1) Find the velocity vector and acceleration vector at t=4s a) in rectangular coordinates b) in cylindrical coordinates c) in natural coordinates (n,t)
Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric vector equation of the plane which passes through these three [3 marks] b) Find the vector cartesian equation of the plane passing through the three points listed [2 marks] c) Hence, or otherwise, find the non-vector cartesian equation of the plane passing through 3 marks] points above. the points above.
Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric...
Question 4 (4 marks) (a) State TWO advantages of using B-spline curve (b) Given a set of data points Po- (0,0,0), P(2,-1,-1), P-(1,2.2) on the curve Q. A B-spline curve calculated by: P(,)-Σ N,,0)I, where N,,0-11 fort, sl < 0 otherwise" 1) Nikiのwith 3 control points and knot vector defined 1-1.) N'서の+ N,,(t)- Itt by [0 0 0 1 1 刂is used to represent the curve. (2 marks) What type of B-spline curve is this? (i) (2 marks) (i) What...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds-
1 point)...
Suppose X is a random vector, where X = (X(1), . . . , x(d))T , d with mean 0 and covariance matrix vv1 , for some vector v ER 1point possible (graded) Let v = . (i.e., v is the normalized version of v). What is the variance of v X? (If applicable, enter trans(v) for the transpose v of v, and normv) for the norm |vll of a vector v.) Var (V STANDARD NOTATION SubmitYou have used 0...
5.0. Protons with kinetic enerigy of 50 MeV are moving in the positive x direction and enter a magnetic B (0.5 T)k directed out of the plane of thepage ure extending from - 0 to -1 m as shown in 29.36. (a) Calculate the y compo nent of the protons momentum as they leave the magnetic field at m. (b) Find the angle a between the initial veloc- ity vector of the proton beam and the velocity vec tor after...
Version 1 0.) Red light propagates through window glass at a speed of 2.0 x 10 m/s. This means that bli light must propagate through vacuum at a speed of: A) 1.5 x 10 m/s B) 2.0 x 10 m/s C) 2.5 x 10 m/s D) 3.0 x 10 m/s E) No way to know with the information given, but it must be <3.0 x 10 m/s A screen red, yellow, blue glass 7.) Red, yellow, and blue light along...