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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- 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 systemEvaluate the dot product A - Bif Ä = 8i – 7j and B = -8i – 5j. ? Ä- B = Submit Request Answer Part B Evaluate the dot product Ä · B it Ä = -8i +8j and B = 5i + 7j. ? A ·B =Problem 1: Let A = î - 2ĵ and B = 2î + ĵ. Compute A.B. Problem 2: Let A = î - 2ĵ and B = 2î + ĵ. Compute A. (A + B). 1 Problem 3: Using the dot product, compute the angle between vectors C and D. C = 2î + 3ĵ D = 3î - 5ĵ
- Q1/ Choose the correct answer (MCQ)? 1. Vector product of two vectors quantities is also known as . . a. scalar product point product 2. The fundamental quantities is called of the- b. dot product d. cross product с. a. Kelvin b. area c. density d. speed 3. A scalar quantity is completely specified by a - a. single direction b. single value c. both4. The dot product of a, · a, is equal to: a. sin 0 cos b. sin o cos 0 c. cos o cos 0 d. sin ø sin 01. 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 ⃗.
- 2. Two vectors A and B are given by à = 2î + 5ĵ + 3k and B = -4î + î + 3k. a. Find the magnitude of Á. || -> b. Find the magnitude of B. c. Find the dot product of the vectors, Á · B. d. Find the angle (smallest) between à & B.o1. If you used only a keyboard to enter data, how many years would it take to fill up the hard drive in a computer that can store 1.0 terabytes of data? Assume 40-hour work weeks, and that you can type 180 characters per minute, and that one byte is one keyboard character. 2. A.) Find the scalar dot product and the angle between the vectors B.) Find the Vector cross product of AxB A = 2.00i + 3.00j + 1.00k B = -4.00i + 2.00j – 1.00kIf the magnitude of the vector product of two vectors a and b are are equal to 0, then what do we know about a and b? a. they are perpendicular Ob. they are in different directions с. they are in different planes O d. They are parallel
- 1. If vectors P = (2i+ 3j+ 6k) cm and Ŕ = (10i - 5j+ 10k) cm, then what is the A. sum of P and Ŕ? B. difference between P and Ŕ? E. magnitude of Ŕ? F. unit vector in the direction of R C. magnitude of P? D. unit vector in the direction of P? G. scalar product of P and R? H. vector product of P and R? 2. A stone is thrown from the top of a building upward at an angle of 30° with the horizontal with an initial speed of 20 m/s. The height of the building is 45.0 m. A. How long does it take the stone to reach the ground? and B. What is the speed of the stone just before it strikes the ground? 3. A wheel is under a constant angular deceleration of 5rad/s2. Its initial speed is 3rad/s. A. What angular distance in rad, rev and degrees will it travel just before coming to rest? B. How long will it travel just before coming to rest? 4. A block with mass m₁ = 6kg that slides on a table with μk = 0.2 is attached by a massless string over a massless, frictionless pulley to a hanging ball with mass…1. Find the dot product of A and B. (Scalar Notation Form) 2. Find the magnitude of the cross product of A and B.E. Engagement Consider the vectors given below A = Azî + Ayĵ + A,k B = Bxî + Byj + B,k Get the dot product of A andB by following the steps below. A·B = (Azî + Ayĵ + A‚k)(Bxî + Byĵ + B,k) Step 1: Multiply the vectors, the way you multiply polynomials. You should get 9 terms. Ā ·B = Step 2: Rearrange your terms. Set side by side the components and the unit vector. A ·B = Step 3: Apply the dot products to your unit vectors. Recall: î · î = j· j = k · k = 1 and î ·j = î · k = j · k = 0 A·B =. Step 4: Write the simplified and the final dot product A·B =