Question 8: [20pt total] Consider the line (1, -3, -1) + t(1,3,2). Q8)a) [12pt] Complete the...
Question 10: [8pt total] Consider the line in 3D space (2,5, 2) +t(-6, 4, 2). 10)a) [4pt] Determine vanishing point of the line when centrally projected onto the plane z = 2: Vanishing point: 10)a)ii) (4pt] Graph the central projection of the line onto the plane z = 2. y 6 2 2 8 -6 -4 -2 0 2 8 -2 61
Question 7: [20pt total] The points (-4,4,2), (4,4, 2), (4, -4,4), and (-4, -4,4) form the vertices of a rectangle in 3D space. Q7)a) [12pt] Complete the below table by calculate the central and parallel projections of these points onto the plane z = 1. Point Central projection onto z=1 Parallel projection onto z (-4,4,2) (4,4,2) (4, -4,4) (-4,-4,4) Q7)b) (8pt] Sketch both the centrally projected rectangle and the parallel projected rectangle on the coordinate planes below (be sure to...
2. Consider the line (t) = (4t + 1,3,2-t) and the ellipsoid + + z2 = 1. What is the distance from the point (-3,3,3) on the line to the point where the line intersects the ellipsoid? a) 8/5 b) (2+ 89)/10 c) (2 - 89)/10 d) 62/V10 e) It makes no sense, the line does not intersect the ellipsoid. 3. Suppose f(x,y) is a function such that f.(0,1) = -3 and f(0, 1) = 8. What is the rate...
Consider the line x (1,3,2) + t(-1,5,-2) Decide which of the following points lie on the line. (There may be more than one.) a) (1,3,2) (1,5,-2) (0, 8, 0) (2,-2,5) b) Which of the following vectors are perpendicular to the line? (There may be more than one.) (2,0,-1) (10,2,0) (3, 4,2) (0,2,5)
Question 1: [10pt total] Consider the line through the points (-3,-4) and (1,4). Q1)a) (3pt) Graph the line on the ey-plane below: 6 4 2 6 4 2 0 2 4 6 2 Q1)b) (3pt] Calculate the equation of the line in the form y=mx+b. Equation of the line: Q1)c) (4pt] Calculate a parametrization of the line. Parametrization of the line:
3. Find the best straight-line fit (least squares) to the measurements t -2, b 4 at at t =-1 b 1 at t0 b 0 at t = 2. Then find the projection p of 3 b 0 onto the column space of A = 1 10 1 2
Find the orthogonal projection of v=[1 8 9] onto the subspace V of R^3 spanned by [4 2 1] and [6 1 2] (1 point) Find the orthogonal projection of v= onto the subspace V of R3 spanned by 2 6 and 1 2 9 projv(v)
4 1 7 1 -3 4 A = -6 8 0 b= . 5 0 3 6 7 2. What is the matrix P describing the orthogonal projection onto R(A), the column space of A?
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...