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QUESTION 1 (Total 15 marks) VECTORS If A -2i+2k and B -3...
please solve 9. Which of the following is an orthogonal pair of vectors? (a) 2i -...
please solve
9. Which of the following is an orthogonal pair of vectors? (a) 2i - ji + k (b) i- j + 2k, -i-j-k (d) 5i + j + k, -i +2j + 3k (e) None of these - **-*-*-* (c) 3i - 2k, 2j - k
3. Consider two vectors u = 2i -j +2k and v=3i+2j-k. (a) Find a vector orthogonal...
3. Consider two vectors u = 2i -j +2k and v=3i+2j-k. (a) Find a vector orthogonal to a and b. _ [3 marks] (b) Show that the vector from (a) is orthogonal to a and b. [1 mark]
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B =...
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
6. 2D vectors Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a)...
6.
2D vectors
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a...
question about linear algebra 21. The following two lines := -i+j+ k + t(2i - 2j - 2k), t e R r and y2 1 = 2 -1 interse...
question about linear algebra
21. The following two lines := -i+j+ k + t(2i - 2j - 2k), t e R r and y2 1 = 2 -1 intersect each other. What is the equation of the line (where s E R) passing through the intersection point of these two lines and perpendicular to both of them? r -ijk s(i - j - k) (a) (b) r i2j+3k + s(i - 2j + 7k) (c) (d) rsik) (e) =j-k s(i...
7. Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b)...
7.
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a unit vector...
6 ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is...
6
ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is in: Provide an example of a) ID b) 2D c) 3D (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? 3,Define a unit vector. Give an example of a unit vector in...
Please help with the following problem and please show all work, thank you. The stress matrix...
Please help with the following problem and please show all work,
thank you.
The stress matrix at a point relative to the xyz coordinate system is given by [25 [0] = | 10 115 10 0 0 15 1 0 | MPa –20] The axes of a new coordinate system XYZ is defined by three vectors X = 2i-2j+k, Y = -i-j, Z= i-j-4k, where i, j, k are the unit vectors along the x, y and z directions. Determine...
• Express the force F as a vector in terms of the unit vectors i, j,...
• Express the force F as a vector in terms of the unit vectors
i, j, and k.
• Determine the angles qx, qy, and qz which F makes with the
positive x-, y-and z-axes.
z, mm B (-25, 50, 40). y, mm ? (15,-20,-25) x, mm
I need only i, j,and k please in clear writing 1. (15 Marks) The following are...
I
need only i, j,and k please in clear writing
1. (15 Marks) The following are body mass index (BMI) scores measured in 1l patients who are free of diabetes and participating in a study of risk factors for obesity Body mass index is measured as the ratio of weight in kilograms to bright in meters squared. 25, 27, 31, 23, 25, 41, 24, 32, 46, 35 and 40 Find the following a) Moan (1 point) b) Median (1 point)...
please solve
9. Which of the following is an orthogonal pair of vectors? (a) 2i - ji + k (b) i- j + 2k, -i-j-k (d) 5i + j + k, -i +2j + 3k (e) None of these - **-*-*-* (c) 3i - 2k, 2j - k
3. Consider two vectors u = 2i -j +2k and v=3i+2j-k. (a) Find a vector orthogonal to a and b. _ [3 marks] (b) Show that the vector from (a) is orthogonal to a and b. [1 mark]
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
6.
2D vectors
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a...
question about linear algebra
21. The following two lines := -i+j+ k + t(2i - 2j - 2k), t e R r and y2 1 = 2 -1 intersect each other. What is the equation of the line (where s E R) passing through the intersection point of these two lines and perpendicular to both of them? r -ijk s(i - j - k) (a) (b) r i2j+3k + s(i - 2j + 7k) (c) (d) rsik) (e) =j-k s(i...
7.
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a unit vector...
6
ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is in: Provide an example of a) ID b) 2D c) 3D (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? 3,Define a unit vector. Give an example of a unit vector in...
Please help with the following problem and please show all work,
thank you.
The stress matrix at a point relative to the xyz coordinate system is given by [25 [0] = | 10 115 10 0 0 15 1 0 | MPa –20] The axes of a new coordinate system XYZ is defined by three vectors X = 2i-2j+k, Y = -i-j, Z= i-j-4k, where i, j, k are the unit vectors along the x, y and z directions. Determine...
• Express the force F as a vector in terms of the unit vectors
i, j, and k.
• Determine the angles qx, qy, and qz which F makes with the
positive x-, y-and z-axes.
z, mm B (-25, 50, 40). y, mm ? (15,-20,-25) x, mm
I
need only i, j,and k please in clear writing
1. (15 Marks) The following are body mass index (BMI) scores measured in 1l patients who are free of diabetes and participating in a study of risk factors for obesity Body mass index is measured as the ratio of weight in kilograms to bright in meters squared. 25, 27, 31, 23, 25, 41, 24, 32, 46, 35 and 40 Find the following a) Moan (1 point) b) Median (1 point)...
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