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Let OAB be a triangle, that is, 0, A and B are not collinear. Now let...
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given...
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
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 ū= (2,4,-1), v = (3.-3,-1) (a) Compute: x ū (b) Compute: ü x 7...
1. Let ū= (2,4,-1), v = (3.-3,-1) (a) Compute: x ū (b) Compute: ü x 7 (c) Is the cross product commutative? If not, what is it instead? 2. Let A = (7, -11,3), B = (1,9, -3), C = (-6,3, -2), D= (0,-8, 12), E = (1, -13,2) (a) Give the vector equation of a line passing through the points A, B. (b) Find the equation of the plane containing the points C,D,E. (c) Find the point of intersection...
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...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
Each of these problems (Problems 1-4) is worth four points Definition: Two lines or curves are said to be normal to each other at their point of intersection if they intersect there at right ang...
Each of these problems (Problems 1-4) is worth four points Definition: Two lines or curves are said to be normal to each other at their point of intersection if they intersect there at right angles or, equivalently, if their tangent lines at the point of intersection are 1. A well-known theorem in geometry states that a line which is tangent to a circle is perpendicular to the radius of the circle at the point of tangency. Use implicit differentiation to...
Mark each statement True or False. Justify each answer. a. A homogeneous system of equations can...
Mark each statement True or False. Justify each answer. a. A homogeneous system of equations can be inconsistent. Choose the correct answer below. O A. True. A homogeneous equation can be written in the form Ax o, where A is an mxn matrix and 0 is the zero vector in R". Such a system Ax -0 always has at least one solution, namely x-0. Thus, a homogeneous system of O B. True. A homogeneous equation cannot be written in the...
Help me solve this please Question Help as An association was formed by wudents to protest...
Help me solve this please
Question Help as An association was formed by wudents to protest wor exploitation in the poor industry. There well as the number of student wrests. The data for S are 18 students for a in in which there was at least one arrest and there free campus organized a niversities. Data were collected for the duration in days of each 's a simple linear regression are found below. Let y be the number of arrests...
To understand how the linear momentum equation is derived from Reynolds transport theorem and to ...
Please answer part c this question has been posted previously
was given the wrong answer
To understand how the linear momentum equation is derived from Reynolds transport theorem and to use the equation to calculate forces. The Reynolds transport theorem(DNDt)syst-aatJcvηρdVtfcsqpVdA relates the change in an extensive quantity N for a system of Lagrangian particles (the left side) to the changes in an intensive quantity η:nm, where m is the mass of the system, in a Eulerian control volume that initially...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
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 ū= (2,4,-1), v = (3.-3,-1) (a) Compute: x ū (b) Compute: ü x 7 (c) Is the cross product commutative? If not, what is it instead? 2. Let A = (7, -11,3), B = (1,9, -3), C = (-6,3, -2), D= (0,-8, 12), E = (1, -13,2) (a) Give the vector equation of a line passing through the points A, B. (b) Find the equation of the plane containing the points C,D,E. (c) Find the point of intersection...
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...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
Each of these problems (Problems 1-4) is worth four points Definition: Two lines or curves are said to be normal to each other at their point of intersection if they intersect there at right angles or, equivalently, if their tangent lines at the point of intersection are 1. A well-known theorem in geometry states that a line which is tangent to a circle is perpendicular to the radius of the circle at the point of tangency. Use implicit differentiation to...
Mark each statement True or False. Justify each answer. a. A homogeneous system of equations can be inconsistent. Choose the correct answer below. O A. True. A homogeneous equation can be written in the form Ax o, where A is an mxn matrix and 0 is the zero vector in R". Such a system Ax -0 always has at least one solution, namely x-0. Thus, a homogeneous system of O B. True. A homogeneous equation cannot be written in the...
Help me solve this please
Question Help as An association was formed by wudents to protest wor exploitation in the poor industry. There well as the number of student wrests. The data for S are 18 students for a in in which there was at least one arrest and there free campus organized a niversities. Data were collected for the duration in days of each 's a simple linear regression are found below. Let y be the number of arrests...
Please answer part c this question has been posted previously
was given the wrong answer
To understand how the linear momentum equation is derived from Reynolds transport theorem and to use the equation to calculate forces. The Reynolds transport theorem(DNDt)syst-aatJcvηρdVtfcsqpVdA relates the change in an extensive quantity N for a system of Lagrangian particles (the left side) to the changes in an intensive quantity η:nm, where m is the mass of the system, in a Eulerian control volume that initially...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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