Resolve F, into components along the u and v axes. Where: F,= 200 N and F,= 300 N Note: Show the parallelogram and the force triangle in the solution. 30 10s
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- Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r, u, and t, respectively. Consider the quantity (3u2t). (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?If 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 parallelshow how to resolve the force F into components acting along the u and v axes using the parallelogram law. Then establish the triangle rule to show FR = F, + F,. Label all known and unknown sides and interior angles. 30° 40° F= 600 N
- AsapIn (Figure 1), l = 4 m and n = 4.5 m. Figure 11 B 8 F=600 N 3 m 1 of 1 Part A Determine the angle between the force and the line AB. Express your answer in degrees to three significant figures. 17 ΑΣΦ 0 = Submit Provide Feedback Request Answer vec ?a.) Find the angle of the sum of the three vectors shown in the figure, measured counterclockwise from the positive x-axis.
- PROBLEM 1 Determine the x and y components of the forces in the figure. 150N 35° 120N ·560 PROBLEM 2 Determine the x and y components of the forces in the figure. 100N SON -480- 40° *Dimensions PROBLEM 3 The cylinder BD exerts on member ABC a force P directed along line BD. Knowing that I must have a 750-N component perpendicular to member ABC, determine: a. The magnitude of the force P, b. Its component parallel to ABC. pEvaluate each of the following. Assume î, ĵ, k are the unit vectors aligne with the x, y, and z axes, respectively. a. î j = d. (4î – j) · (3î + 5j – 10k) = b. k - k= c. k- î=If the magnitude of the vector product of two vectors a and b are are equal to ab, then what do we know about a and b? a. They are parallel O b. they are in different directions O c. they are perpendicular O d. they are antiparallel
- The Vector Product Two vectors lying in the xy-plane are given by the equations A = 8î + 2j and B = -3î + 3j. Find Ax B and verify that à ×B = -B x A. SOLUTION Conceptualize Given the unit-vector notations of the vectors, think about the directions the vectors point in space. Draw them on graph paper and imagine the parallelogram for these vectors. Categorize Because we use the definition of the cross product discussed in this section, we categorize this example as-Select-- problem. Write the cross product of the two vectors: AxB = î + 2j ) x î + 3j Perform the multiplication: ĀxB = 8î x (-3î) + 8î × 3j +| j x (-3î) + 2j x Use the equations for the cross product of unit vectors to evaluate the various terms: AXB = To verify that AxB = -B x A, evaluate Bx A: BxA = (-31 + Perform the multiplication: BxA = (-31) x ]î +(-3î) × 2j + 3ĵ × 8î + j x 2j Use the equations for the cross product of unit vectors evaluate the various terms: BxA = Therefore, Ax B = -B xA As an alternative method for…Illustrate the given vectors below. Use protractors if you have. If you don't have, you are allowed to estimate the angle of the vector with respect to its origin and the x-axis.Determine the magnitude and direction of the cross product r × F if F = 30.0 N, 36.9° North of East and r =2.00 m, 30° West of North. Assume that z-axis is the axis perpendicular to this paper.