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15. Determine the following: a) Determine the vector equation of the plane that contains the following...
Solve the following problems. Submit the written solution and a GeoGebra file. A. Determine a vector equation for the plane that contains the following two lines. 11:r = (2,4,-2) + t(1,-1,3), t E R 12:7 = (2, 4,-2) + s(3, 2,-2),s E R (2,4,-2)+11 ',-1,5) +S(5,2,-2) か B. Find the angle between these lines. C. Determine the corresponding Cartesian equation of this plane. D. Determine the distance between point Q(2,2,-1) and Line 1. E. Determine the coordinates of the point...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
please answer question 4-7 Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
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...
1. (15 points) (a) (5 points) Find the equation of the plane a that contains points A(1,5,4) B(1,0, 1) and C(4, 0,5) (b) (5 points) Find the distance from the point D(2, 1,7) to this plane (c) (5 points) If plane 3 has equation y -3z+2x = 5, find a unit vector that is parallel to the intersection of a and B.
Find general equation of the plane containing the following two lines: x = 2t - 4 2t + 1 =t+3 5,12 and L2: y = -t y 2 - 5t - 1 2
K to browse... Q3 (8 points) Find general equation of the plane containing the following two lines: = 2t - 4 ci : y 2t +1 = -t+3 5t+2 and L2: y z 5 - 1
АЗ. You are given that the plane P contains both the point and the line Ls, where Q has position vec- tor q = i + 3, and L3 is given by the equation r = (0, i, 2) + λ(1, 3,-1) (where λ is a real parameter). i) Write down two vectors representing two different directions which lie in the plane P. [2 marks i) By using the cross product or otherwise, find a direction perpendicular to the plane....
x =-y+2 = -z+2 The symmetric equations for 2 lines in 3-D space are given as: 1. L,: x-2 = -y+1 = z+1 a) Show that lines L1 and L2 are skew lines. b) Find the distance between these 2 lines x =1-t y=-3+2t passes through the plane x+ y+z-4=0 2. The line Determine the position of the penetration point. a. Find the angle that the line forms with the plane normal vector n. This angle is also known as...
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...