CHAPTER 1 INTRODUCTION AND MATHEMATICAL CONCEPTS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (d) The resultant vector R is drawn from the tail of the first vector to the head of the last vector. 2. (c) Note from the drawing that the magnitude R of the resultant vector R is equal to the shortest distance between the tail of A and the head of B. Thus, R is less than the magnitude (length) of A plus the magnitude of B. 3. (b) In this drawing the vector –C is reversed relative to C, while vectors A and B are not reversed. 4. (c) In this drawing the vectors –B and –C are reversed relative to B and C, while vector A is not reversed. 5. (c) When the two vector components Ax and Ay are added by the tail-to-head method, the sum equals the vector A. Therefore, these vector components are the correct ones. 6. (b) The displacement vector A points in the –y direction. Therefore, it has no scalar component along the x axis (Ax = 0 m) and its scalar component along the y axis is negative. 7. (e) The scalar components are given by Ax′ = −(450 m) sin 35.0° = −258 m and Ay′ = −(450 m) cos 35.0° = −369 m. 8. (d) 9. Rx = 0 m, Ry = 6.8 m 10. R = 7.9 m, θ = 21 degrees 11. (a) The triangle in the drawing is a right triangle. The lengths A and B of the two sides are known, so the Pythagorean theorem can be used to determine the length R of the hypotenuse. 12. (b) The angle is found by using the inverse tangent function, 1 4.0 km tan 53 3.0 km θ − ⎛ ⎞ = =° ⎜ ⎟ ⎝ ⎠