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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 L respectively. Consider the quantity (-3 2t ). (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?9) Consider vector A = (7, 5) and vector B = (−3, −4). a) What is the direction and magnitude of vector A? b) What is the direction and magnitude of vector B? c) What is the direction and magnitude of vector C = A + B?1. Please refer to the following vectors:A = 6i + 2j - 3kB = 3i - j - 2kC = -i + j - 4kD = j - 3kE = -i + 2kF = -5kG = 2iH = -3jI = -4i +4j Find the projection of vector C on vector D. CHOICES: 5 11 13 25 2. For bodies that are falling, to achieve terminal velocity, what must happen to the acceleration of the body? a. The acceleration of the body is remains the same through time. b. The acceleration of the body must decrease over time c. The acceleration of the body must equal to the acceleration due to gravity. d. The acceleration of the body must increase over time.
- Vector v = <1,1,0> and vector w = <-1,-1,sqrt2>. What is the angle between v and w in degrees?1. Let θ be the angle that the vector ? makes with the +x-axis, measured counterclockwise from that axis. Find angle θ for a vector that has these components: (a) Ax = 2m, Ay = -1m; (b) Ax = 2m, Ay = 1m; (c) Ax = -2m, Ay = 1m; Ax = -2m, Ay = -1m.A = 3i + 4j - 5k and B = -2j + k. a) | 2A - B | b) Vectors A and BWhat is the angle between?
- 2)Given the vectors A =3 î +2 ĵ and B = î -3ĵ a-Calculate the vector sum M=A+B and the vector difference N= A-B in terms of unit vectors. b- Find the direction and magnitude of the vectors M and N. 3)The polar coordinate of (r, θ ) of a Cartesian coordinate (-3.5,-2.5) is: a) (4.3, 216o ) b) (10, 100o ) c) (120, 17o ) 4)Two vectors are given as a= i +2j+2k and b=2i+4j+2k . Vector c which satisfies the relation a-b+c=3i is: a) i+3j b) –i +j c) -i+5j d) 4i+2jAt a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 8.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 55.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball? yards (b) What if? The receiver that catches the football travels 64.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 7.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 50.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball?What if? The receiver that catches the football travels 65.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?
- Vector B→B→ has magnitude 7.30 and direction 14.0° below the +x-axis. Vector C→C→ has x-component Cx = −2.00 and y-component Cy = −6.70. a. What is the x-component of B→B→ ? b.What is the y-component of B→B→ ? c. What is the magnitude of C→C→ ? d. What angle does C→C→ make with the +x-axis in counterclockwise direction? A positive angle is counterclockwise from the +x-axis anwer in degrees e. What is the magnitude of C→+B→C→+B→ ? f. What angle does the resultant vector C→+B→C→+B→ make with the +x-axis in clockwise direction? A positive angle is counterclockwise from the +x-axis. asnwer in degrees g. What is the magnitude of C→−B→C→-B→ ? h. What angle does the vector C→−B→C→-B→ make with the +x-axis in counterclockwise direction? A positive angle is counterclockwise from the +x-axis. asnwer in degrees i. What is the x-component of C→−B→C→-B→ ? j.What is the y-component of C→−B→C→-B→ ?Please refer to the following vectors:A = 6i + 2j - 3kB = 3i - j - 2kC = -i + j - 4kD = j - 3kE = -i + 2kF = -5kG = 2iH = -3jI = -4i +4j Which of the following pairs of vectors are PERPENDICULAR to each other?I. A and BII. F and GIII. G and HIV. C and I CHOICES OF ANSWERS: I and II II and III II, III, and IV All of them No AnswerVector A has components ax= -3.0 m/s^2 and ay= +4.0 m/s^2 a. What is the magnitude and direction of vector A? b. What is the direction of vector A? Give an angle with respect to one of the coordinate axes
