1.)Two vectors, vector d2? ½ vector d1 and vector d2? m2 (c) What is the angle b

Question

1.)Two vectors, vector d2? ½ vector d1 and vector d2? m2 (c) What is the angle between vector d1 ? vector d2? m2 (b) What is vector d1 ½ vector d2 is in the xz plane 30½ from the positive direction of the x axis, has a positive z component, and has magnitude1.80 m. (a) What is vector d1 is in the yz plane 70.0½ from the positive direction of the y axis, has a positive z component, and has a magnitude of 4.50 m. Displacement k hat. 3.)Displacement j hat + 6.0 i hat + 3.0 k hat and b = 6.0 j hat + 2.0 i hat + 5.0 s with arrow 2.)Use the definition of scalar product, a½b = ab cos ?, and the fact that a½b = axbx + ayby + azbz to calculate the angle between the two vectors given by a = 1.0 r with arrow ? s with arrow (b) r with arrow ½ s with arrow, lie in the xy plane. Their magnitudes are 4.50 and 7.00 units, respectively, and their directions are 320½ and 85½, respectively, as measured counterclockwise from the positive x axis. What are the values of the following products? (a) r with arrow ans

Explanation / Answer

1)

|r| = 4.50

|s| = 7.00

r = 4.5*cos(320)i + 4.5*sin(320)j

r = 3.4472 i - 2.8925 j

s = 7*cos(85) i + 7*sin(85)j

s = 0.61 i + 6.9733 j

a)

r.s = 3.4472*0.61 - 2.8925*6.9733

r.s = -18.067

rxs = (3.4472 ,- 2.8925)x(0.61 , 6.9733)

rxs = 25.8028

2)

a = (1,5,2)

b = (6,3,6)

a.b = 1*6 + 5*3 + 2*6

a.b = 33

|a| = sqrt(1^2 + 5^2 + 2^2)

|a| = 5.477

|b| = sqrt(6^2 + 3^2 + 6^2)

|b| = 9

cos(a,b) = a.b / |a| |b|

cos(a,b) = 33 / (9*5.477)

cos(a,b) = 0.66946

angle between a and b = acos(0.66946)

= 47.974 degrees

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