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D. Explain why the vectors in the following form describe a plane (where both t and s are parameters): Then find an equation for the plane deeribed by these veetors. D. Explain why the vectors i...
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters) t1,0,3 +s<1,1,-2 Then find an equation for the plane described by these vectors D. Exp...
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters) t1,0,3 +s<1,1,-2 Then find an equation for the plane described by these vectors
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters) t1,0,3 +s
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
АЗ. You are given that the plane P contains both the point and the line Ls, where Q has position ...
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....
it veetors délfhed above 2) Find the length of vector i-2 3 s 3) Let u--3...
it veetors délfhed above 2) Find the length of vector i-2 3 s 3) Let u--3 v 3 2l, and w [5 -1l 2 a) Treating u, v', and w, as vectors, are the inner products uw, v,u, and 1.w, defined? If yes, compute them. If any of them is not defined, explain why not. b) Treating u,v, and w' as matrices, are the products n', p'u and zm defined? If yes, compute them. If any of them is not...
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6 Find the equation of the plane that...
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6
C) 41.5 D) 50.9 24 In the xy-plane, the graph of a linear equation of the...
C) 41.5 D) 50.9 24 In the xy-plane, the graph of a linear equation of the form y =mx+ b and the graph of an exponential equation of the form y = ab* both contain points (1,3) and (2,4). If the point (r, s) is on the graph of the linear equation and the point (r, t) is on the graph of the exponential equation, where 0 < r< 4 and s > t,which of the following must be true?...
The coordinates of a kite in the xy plane are x(t)=At and y(t)=3.0m -Bt2 where a=2.4m/s...
The coordinates of a kite in the xy plane are x(t)=At and y(t)=3.0m -Bt2 where a=2.4m/s and B=1.2m/s2. Find vectors v(t), a(t) and magnitudes at 2.0s Possible Answers: ........1: vectors v(t)=A i - 2Bt j, a(t)= -2B j, and magnitude v(2.0s) = -4.8m/s ........2: vectors v(t)=A i - 4Bt j, a(t)= -2B j, and magnitude v(2.0s) = 4.8m/s ........3: None of the above
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i =...
(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...
Find a basis for the following plane in R3 1 + y - 2z = 0...
Find a basis for the following plane in R3 1 + y - 2z = 0 First, solve the system, then assign parameters s and t to the free variables in this order), and write the solution in vector form as su + tv. Below, enter the components of the vectors u - (un, uz, uz)and v = (1, 0, vy)". ty and U-
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...
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, t--1.5 (2,5,8) s 3, t-1 s-3, t--2 What values of s and t correspond to point O? What values of s and t correspond to point D? What values of s and t correspond to point B? what values of s and t correspond to point C?...
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters) t1,0,3 +s<1,1,-2 Then find an equation for the plane described by these vectors
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters) t1,0,3 +s
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
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....
it veetors délfhed above 2) Find the length of vector i-2 3 s 3) Let u--3 v 3 2l, and w [5 -1l 2 a) Treating u, v', and w, as vectors, are the inner products uw, v,u, and 1.w, defined? If yes, compute them. If any of them is not defined, explain why not. b) Treating u,v, and w' as matrices, are the products n', p'u and zm defined? If yes, compute them. If any of them is not...
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6
C) 41.5 D) 50.9 24 In the xy-plane, the graph of a linear equation of the form y =mx+ b and the graph of an exponential equation of the form y = ab* both contain points (1,3) and (2,4). If the point (r, s) is on the graph of the linear equation and the point (r, t) is on the graph of the exponential equation, where 0 < r< 4 and s > t,which of the following must be true?...
(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...
Find a basis for the following plane in R3 1 + y - 2z = 0 First, solve the system, then assign parameters s and t to the free variables in this order), and write the solution in vector form as su + tv. Below, enter the components of the vectors u - (un, uz, uz)and v = (1, 0, vy)". ty and U-
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, t--1.5 (2,5,8) s 3, t-1 s-3, t--2 What values of s and t correspond to point O? What values of s and t correspond to point D? What values of s and t correspond to point B? what values of s and t correspond to point C?...
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