![5. Let u = [0,1,1), v= (-5, -4,6.7], and P = (4, -5,6). In the following, when rounding numbers, round to 4 decimal places. (](http://img.homeworklib.com/questions/0c83cd60-000b-11eb-ba76-fff143d59cba.png?x-oss-process=image/resize,w_560)
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![(5 12. [-s, -4,47] 31. [0,?,] pa 4-5,6) ů fara meteric equation of the plane Pi, ñ = (4.-5,6) + $(011) ++(-5,-4, 6-7) where s](http://img.homeworklib.com/questions/8bc200e0-1181-11eb-abc3-4bed26ec8a7f.png?x-oss-process=image/resize,w_560)
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5. Let u = [0,1,1), v= (-5, -4,6.7], and P = (4, -5,6). In the following,...
5. Let u = [0,1,1), v = (-5, -4,6.7), and P = (4.–5.6). In the following,...
5. Let u = [0,1,1), v = (-5, -4,6.7), and P = (4.–5.6). In the following, when rounding numbers, round to 4 decimal places. (i) Find the parametric form of the equation of the plane P. containing P and with direction vectors u and v. (ii) Find the parametric form of the equation of one of the two planes that are parallel to P, and distance 1 away from P1.
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx...
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 72 = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 4. Solve the following system of linear equations using Gauss-Jordan elimination: x1 + x2 - 2.13 + 24 +3.25 = 1 2.x1 - x2 +...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
1. Let Q = (-3.-3.-3.3), R = (-3.-3,-33) and S = (1,10,10.1). In the following, when...
1. Let Q = (-3.-3.-3.3), R = (-3.-3,-33) and S = (1,10,10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QR and RS. (ii) Find the angle in degrees between QR and RS. (iii) Find ||QŘ|| and ||RŠI. (iv) Find the projection of R$ onto QR. 2. Let v = [6, 1, 2], w = [5,0,3), and P = (9,-7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle betwe...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
1. Let Q = (-3, -3, -3.3), R = (-3, -3, -33) and S = (1,...
1. Let Q = (-3, -3, -3.3), R = (-3, -3, -33) and S = (1, 10, 10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QŘ and RS. (ii) Find ||QR|| and ||RŠI. (iii) Find the angle in degrees between QR and RS. (iv) Find the projection of RŠ onto QŘ. 2. Let v= [6, 1, 2], w = [5,0,3], and P = (9, -7,31). (i) Find a vector u orthogonal to both v...
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.)...
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
Part c and d Question 5 (30 marks) Let A1, B(3,-5,0) and C(-1,4,1) be three points...
Part c and d
Question 5 (30 marks) Let A1, B(3,-5,0) and C(-1,4,1) be three points in R. Use vector method(s) to solve each of the following. R-8 (a) Find the unit vector u in the direction of AB-3AC. (b) Calculate the smaller angle betwen AB and AC. Correct the answer to ONE decimal place. (c) Find the shortest distance between B and the line passing through A and C. Correct the answer to ONE decimal place. (Hint: Consider the...
Find the parametric equation of the line in R3 in the direction v-(2,1,3) and containing the...
Find the parametric equation of the line in R3 in the direction v-(2,1,3) and containing the point P (-1,3,4). Find the angle between the vectors P and U.
5. Let u = [0,1,1), v = (-5, -4,6.7), and P = (4.–5.6). In the following, when rounding numbers, round to 4 decimal places. (i) Find the parametric form of the equation of the plane P. containing P and with direction vectors u and v. (ii) Find the parametric form of the equation of one of the two planes that are parallel to P, and distance 1 away from P1.
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 72 = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 4. Solve the following system of linear equations using Gauss-Jordan elimination: x1 + x2 - 2.13 + 24 +3.25 = 1 2.x1 - x2 +...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
1. Let Q = (-3.-3.-3.3), R = (-3.-3,-33) and S = (1,10,10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QR and RS. (ii) Find the angle in degrees between QR and RS. (iii) Find ||QŘ|| and ||RŠI. (iv) Find the projection of R$ onto QR. 2. Let v = [6, 1, 2], w = [5,0,3), and P = (9,-7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
1. Let Q = (-3, -3, -3.3), R = (-3, -3, -33) and S = (1, 10, 10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QŘ and RS. (ii) Find ||QR|| and ||RŠI. (iii) Find the angle in degrees between QR and RS. (iv) Find the projection of RŠ onto QŘ. 2. Let v= [6, 1, 2], w = [5,0,3], and P = (9, -7,31). (i) Find a vector u orthogonal to both v...
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
Part c and d
Question 5 (30 marks) Let A1, B(3,-5,0) and C(-1,4,1) be three points in R. Use vector method(s) to solve each of the following. R-8 (a) Find the unit vector u in the direction of AB-3AC. (b) Calculate the smaller angle betwen AB and AC. Correct the answer to ONE decimal place. (c) Find the shortest distance between B and the line passing through A and C. Correct the answer to ONE decimal place. (Hint: Consider the...
Find the parametric equation of the line in R3 in the direction v-(2,1,3) and containing the point P (-1,3,4). Find the angle between the vectors P and U.
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