(a)
The magnitude of the scalar components of the vector
(a)
Answer to Problem 38PQ
The magnitude of the scalar components of the vector
Explanation of Solution
Given vector is
Write the general form of a vector (say
Here,
Compare the given vector with the general form to deduce its scalar components.
Conclusion:
Therefore, the magnitude of the scalar components of the vector
(b)
The magnitude of the vector
(b)
Answer to Problem 38PQ
The magnitude of the vector
Explanation of Solution
Given vector is
Write the expression for the magnitude of the vector
Conclusion:
Substitute
Therefore, the magnitude of the vector
(c)
The angles that the vector
(c)
Answer to Problem 38PQ
The angles that the vector
Explanation of Solution
Given vector is
In order to find the angle that the vector make with the coordinate axes, a right triangle can be formed with vector
Here,
Here,
Here,
Solve equation (I) for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the angles that the vector
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Chapter 3 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. Use the analytical method to determine the following: (a) Find his net displacement vector. (b) How far is the restaurant from the post office? (c) If he returns directly from the restaurant to the post office, what is his displacement vector on the return trip? (d) What Is his compass heading on the return trip? Assume the +x-axis is to the east.arrow_forwardA Three vectors all have the same magnitude. The symbol for the magnitude of each of these vectors is M. The first vector A points in the positive x direction. The second vector B points in the negative y direction. The third vector C points in the positive z direction. These three vectors added together are equal to a fourth vector D. What is the magnitude of the fourth vector?arrow_forwardAt one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?arrow_forward
- Vector F is proportional to vector A such that F=mA and m is a scalar. a. If A=2.4+3.0j and F=4.0+5.0j, what is m? b. Why is it impossible to have A=2.4+3.0j and F=4.0+0.50j, given the relationship between the two vectors?arrow_forwardFor each of the following velocity vectors, give the vector component, the scalar component, and the magnitude. a. v=35.0jm/s b. vx = 53.0 m/s c. vz = 3.50 m/s d. v=5.30m/sarrow_forwardA baseball diamond consists of four plates arranged in a square. Each side of the square is 90 ft (27.43 m) long. Use an x y coordinate system with the origin at the center of the diamond as shown in Figure P3.18. a. What is the position of each plate in this system? b. What is the distance from home plate to second base?arrow_forward
- u = 4i – ĵ + 3k v = 2î + j+k -i+sj+3k r= ai + Bj+ yk 6. w = Evaluate the scalar products u.v and v.w. Evaluate u.w and interpret the result. If u and v are both perpendicular to r, find a unit vector in the direction of r (without using the vector product). Find the angle between u and v.arrow_forwardMoving to another question will save this response. Question 6 Given two vectors A = 7i+ 5j - 2k, and B = 3i – 10j + 6k, what is the angle between the two vectors? O A. 112.7° B. 116.3° O C. 118 4° O D. 115° O E. None of these Moving to another question will save this response.arrow_forwardThe grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled A⃗ A→ through D⃗ D→. This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. A. What is the xcomponent of A→? B.What is the y component of A⃗ ? C.What is the y component of B⃗ ? D.What is the x component of C⃗ ? E. In ordered pair notation, write down the components of vector B⃗ F. In ordered pair notation, write down the components of vector D G.What is true about B⃗ and D⃗ ? They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors.arrow_forward
- a. What are the x- and y-components of vector E→ shown in terms of the angle θ and the magnitude E? b. For the same vector, what are the x- and y-components in terms of the angle Φ and the magnitude E?arrow_forwardVector A has a magnitude 28 and points to the east. Vector B has a magnitude 19 and points north. a. What is the magnitude of the vector sum A and B? b. What is the direction of the vector sun of A and B in degrees?arrow_forwardA particle moves along a space curve C with a vector is given by F(t) = 3 cos 2t ê, + 3 sin 2t ê2+ (8t - 4)ês 5. a. Find a unit tangent vector T to the curve C. b. Show thati = vĩarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University