Magnitude of vectors
Homework Answers
The magnitude of a vector is given by the square root of the sum of the squares of its components. (basically the Pythagorean theorem in 3-D)
M=sqrt(x2+y2+z2)
so
i. M=sqrt(9+25+4)=sqrt(38)=6.16
ii. M=sqrt(9+25+4)=6.16
iii. M=sqrt(9+25+4)=6.16
iv. M=6.16 again
they are all equal
i=ii=iii=iv
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j +...
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j - kand C i + 2j - 2k, find: ax (b x c) (ax b) x t i. ii
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j -...
Two vectors A = -3i + 4 - 2k and B = 5j + 2k act...
Two vectors A = -3i + 4 - 2k and B = 5j + 2k act on an object. Determine: (a) the magnitude of A (b) the magnitude of B A.B (c) the angle between A and B
Two vectors A = -3i + 4j - 2k and B = 5j + 2k act...
Two vectors A = -3i + 4j - 2k and B = 5j + 2k act on an object. Determine: (a) the magnitude of A the magnitude of B A: B the angle between A and B
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...
Using the definition of the scalar product, find the angle between the following vectors. (Find the...
Using the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A = 6i - 7j and B = 8i - 5j [17.33] (b) A = 3i + 3j and B = 3i - 4j + 2k (c) A = i - 2j + 2k and B = 3j + 4k
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...
Consider the three displacement vectors A = (3i - 3j) m, B = (i - 4j)...
Consider the three displacement vectors A = (3i - 3j) m, B = (i - 4j) m, and C = (2i + 5j) m. Use the component method to determine (a) the magnitude direction of the vector D = A + B + C and (b) the magnitude and direction of E = -A - B + C. A person going for a walk follows the path shown in Figure P1.51. The total trip consists of four straight-line paths. At...
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...
Using the definition of the scalar product, find the angle between the following vectors. (Find the...
Using the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A = 7i − 8j and B = 3i − 5j ° (b) A = −3i + 6j and B = 3i − 4j + 2k °
5. Find the i) scalar and ii) vector projections of v onto u if u =...
5. Find the i) scalar and ii) vector projections of v onto u if u = 7i+j – 2k and v= 3i -5j +2k
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j - kand C i + 2j - 2k, find: ax (b x c) (ax b) x t i. ii
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j -...
Two vectors A = -3i + 4 - 2k and B = 5j + 2k act on an object. Determine: (a) the magnitude of A (b) the magnitude of B A.B (c) the angle between A and B
Two vectors A = -3i + 4j - 2k and B = 5j + 2k act on an object. Determine: (a) the magnitude of A the magnitude of B A: B the angle between A and B
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...
Using the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A = 6i - 7j and B = 8i - 5j [17.33] (b) A = 3i + 3j and B = 3i - 4j + 2k (c) A = i - 2j + 2k and B = 3j + 4k
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...
Consider the three displacement vectors A = (3i - 3j) m, B = (i - 4j) m, and C = (2i + 5j) m. Use the component method to determine (a) the magnitude direction of the vector D = A + B + C and (b) the magnitude and direction of E = -A - B + C. A person going for a walk follows the path shown in Figure P1.51. The total trip consists of four straight-line paths. At...
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...
5. Find the i) scalar and ii) vector projections of v onto u if u = 7i+j – 2k and v= 3i -5j +2k
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