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- 4), D1.4. The three vertices of a triangle are located at A(6, -1, 2), B(-2, 3, and C(-3, 1, 5). Find: (a) RAB × RAC; (b) the area of the triangle; (c) a unit vector perpendicular to the plane in which the triangle is located. Ans. 24ax +78ay + 20az; 42.0; 0.286ax +0.928ay +0.238azIn the figure below, find each of the following. 5.00 3.00 4.00 (a) the side opposite 0 (b) the side adjacent to p (c) cos 0 (d) sin o (e) tan pDATE: i.) Find the Liestion of given necto the Measure the angle wilth Mopect to the tx-axis coun terclockwise only gire the numei cal value. 3.)A vector has a magnitude 31 ¢ blase is in quadrant. 58.9°W/ reepect to thie + y-ais. What i the x- * the vector ? w on ongle companent.
- Two vectors A 6 units and B=8 units. If A B = 10 then the angle between the two vectors is O a 78 Ob. 58 OE 65° Od S1°Convert the following Vectors given in polar coordinates (r, q) to the equivalent Vector in cartesian coordinates (x, y). Check significant figures. C = (12.0, 34) b. F = (5.00, 45.0o )For the vectors A = (3.0m).ı+(4.0m).j and B = (5.0m).ı+(-2.0m).j,find the results of the vector operations given below; A) C = A+2B ; find the vector C and its mahnitude. B) Find the angle between the vector C and the unit vector j.
- Solution: The projectile motion equations: x = x₁ + (vo cos 0) t y = yo + (vo sin 0o) t - 1/2gt² Call the starting point (xo, yo) = (0,0). To find (x, y) for the ending point, use triangle trig on the hill angled at 20°: x = d cos 20° = .940d and y = d sin 20° = .342d Plug in: .940d = (vo coso) t (Eqn. 1) .342d = (vo sin 0o) tgt² (Eqn. 2) The variable t is not mentioned in the problem. We can remove it by solving Eqn. 1 for t and plugging into Eqn. 2: t = .940d vo cos 00 .940d vo cos o -) - 12/19 ( Cleaning up and plugging in g = 9.8m: .342d = (v₁ sino) ( .940d vo cos 00 201.18 If Č is the vector sum of Å and B, Č = Å + B, what must be true about the directions and magnitudes of A and B if C = A + B? What must be true about the directions and mag- nitudes of Á and B if C = 0?Vector has a magnitude of 44 units and points in the positive y direction. When vector is added to , the resultant vector points in the negative y direction with a magnitude of 25 units. Find the magnitude and direction of B. 396.267 magnitude Your response differs from the correct answer by more than 100%. unit(s) 355.463 direction Your response differs from the correct answer by more than 10%. Double check your calculations.º counterclockwise from the +x-axis
- A small plane flies 40.0 km ma direction 60 north of east and then flies 30.0 km in a direction 15 north of east. Use the analytical method to find the total distance the plane covers from the starting point, and the geographic direction of its displacement vector. What is its displacement vector?A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts around one- half of the circle, starting from the west point, find (a) the magnitude of his displacement vector and (b) how far he actually skated. (c) What is the magnitude of his displacement vector when he skates all the way around the circle and comes back to the west point?7. YA 60° A = 10.0 30° B 30° 53° D = 20.0 37° C = 12.0 10 F = 20.0 B = 5.0