1. Using the figure below, a. Expressed in terms of i and j unit vectors, what is the vector result of A + VB/A? b. Expressed in terms of i and j unit vectors, what is the vector result of F₁+F₂? c. What is the dot product of (VA + VB/A) · (F₁ + Ē₂ ) ? d. What is the dot product of F₂ · VB/A? VB/A F₁ 60° B A X VA Vector Magnitudes |VA| = 10 m/s ||BA| = 7 m/s ||₁|= 120 N ||F₂| = 50 N
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- How many cubic centimeters (cm3) are in one cubic meter (m3)?5. Compute the x and y components of the vectors A, B, and C in the figure below. 6. Add the following displacements by the component method 8.0 ft. directed 45° northeast, 12.0 ft. directed south, and 20.0 ft. directed 45° directed south of west. 7. Find the scalar product of two vectors A=4/+3j and B=5i-2j 8. Find the angles between vectors given in Problem 7 9. Find the vector product of vectors given in Problem 7 10. What is the magnitude of the vectors product in Problem 9?Two vectors in Cartesian coordinates have components A=(2,3,2) and B=(4,-1,7). What is the dot product of vector A with vector B? A•B=
- 2. (a) Find the magnitude of the vector −2î + ĵ + 2k̂). (b) Find the magnitude of the vector 3î− 6ĵ + 2k̂). (c) Find the angle between these two vectors. (d) Calculate the vector sum of the vectors. (e) Calculate the dot product of the vectors. (f) Calculate the cross product of the vectors. Need help with d to f. Attach here are the given and answers to previous questions.1. Find the dot product of A and B. (Scalar Notation Form) 2. Find the magnitude of the cross product of A and B.2. (a) Find the magnitude of the vector −2î + ĵ + 2k̂). (b) Find the magnitude of the vector 3î− 6ĵ + 2k̂). (c) Find the angle between these two vectors. (d) Calculatethe vector sum of the vectors. (e) Calculate the dot product of the vectors. (f) Calculatethe cross product of the vectors.
- Problem 20: Assume you have two vectors, A = 7.1i + 3.9j and an unknown vector B with length 3.2. In this problem, you must assume that both components of B are positive, Bx > 0, and By > 0. Part (a) If the scalar product of these two vectors is A⋅B = 16.3, what is the x-component of the vector B? You may assume that Bx > 0. Part (b) What is the y-component of the vector B? Again, assume By > 0.1. Three vectors are oriented as shown. If | A ⃗ | = 120 units, | B ⃗ | = 40 units and | C ⃗ | = 30 units a) Find the resultant vector, its size and direction. b) Calculate the magnitude and direction of B ⃗ × C. c) Calculate the scalar product of (A ⃗ + B ⃗) ∙ C ⃗.wo vectors have the following magnitude, A = 14.8 m and B = 14.5 m. Their vector product is: A⨯B = -1.1 m i + 9.7 m k. What is the angle (in degrees) between the vectors A and B? Hint: Use |A⨯B| = AB sin(θ) Note: Bold face letters represents a vector.
- A vector A = 1ax+1ay, the origin of this vector is the point M (1, 0.5, 1) in Cartesian coordinate system. a. Determine the component of the vector A in the direction of the vector ax b. Determine the dot product A.ay c. Determine cross product A.az d. Determine the angle formed by the vector A and the vector ay. e. Determine the componen ts of this vector in cylindrical coordinate system f. Determine the components of this vector in spherical coordinate systemGiven three vectors A = -2i + 3j + 4k, B = 3i + 1j – 3k and C = 3i -4j + 2k, do the following: a) Find the magnitude of each vectorb) Write an expression for the vector sum A + B using unit vectorsc) Write an expression for the vector difference A – C using unit vectorsd) Find the scalar product A ∙ Be) Find the cross product A × Bf) Find the angle between A and Bg) Find (A x C) ∙ BTwo vectors A and B in two dimensions are given by A = 2i + 3j and B = - i + 4 Find the magnitudes of A and B, the scalar (or dot) product of A and B and the angle between A and B. (Hint: For the last part, the scalar product of two vectors can be expressed in terms of components and also in terms of the angle between the vectors. i and j are unit vectors along x- and y- directions.) a.) |A| = 6, |B| = 4.1, A.B = 10, θ = 47.40. b.) |A| = 2.2, |B| = 1.7, A.B = 3.2, θ = 31.20.