Vectors and the dot product: components, projection, work

1. 1A force of 325N at 35 degree to the horizontal in Cartesian form

   1. A[266.22 , 186.41]
   2. B[186.41 , 266.22]
   3. C[-20.08 , 28.67]
   4. D[28.67 , -20.08]
2. 2[3 , -2]is collinear with [6 , -4]

   1. ARichtig
   2. BFalsch
3. 3A person pushes a lawnmower with a force of 325 N. The handle makes an angle of 55 degree with the ground. There is a force [blank_start][186.41 , 266.22][blank_end] in component form as a Cartesian vector.

   1. A[186.41 , 266.22]
4. 4Determine the value of k so that u=[2 , 5] and v=[k , 4] are perpendicular

   1. Ak=10
   2. Bk=20
   3. Ck=-20
   4. Dk=-10
5. 5The dot product is defined as a*b=|a||b|sin & , where & is the angle between a and b, 0 smaller than\equal & smaller than\equal 180 degree.

   1. ARichtig
   2. BFalsch
6. 6Triangle ABC {A(3 , 1) , B(-2 , 3) , C(5 , 6)} is a right-angled triangle. Angle CBA is right-angle

   1. ARichtig
   2. BFalsch
7. 7Determine the projection of u of v (u=5) (v=1)angle is 50 degree

   1. A3.21
   2. B5 sin50 degree
8. 8Bill applies a force at 35 degree to the horizontal to move a football tackling dummy 5 m horizontally. He does 120 J of mechanical work. The magnitude of the force is [blank_start]29.3[blank_end]N

   1. A29.3
9. 9A shoe store sold 400 pairs of Excalibur shoes and 300 pairs of Camelot shoes in a year. Excalibur shoes sell for $120 and Camelot shoes sell for $220. The dot product s*p is [blank_start]114000[blank_end].

   1. A114000
10. 10Proj V on U = ( U * V / V * V ) V

    1. ARichtig
    2. BFalsch

11. 11if u=[U1, U2, U3] and v=[V1, V2, V3], then u-v=[U1-V1, U2-V2, U3-V3]

    1. ARichtig
    2. BFalsch
12. 12For two 3-D Cartesian vectors, u=[U1, U2, U3] and v=[V1, V2, V3] , [blank_start]u*v=U1V1+U2V2+U3V3[blank_end]

    1. Au*v=U1V1+U2V2+U3V3
13. 13Determine all unit vectors collinear with[4, 1, -7]

    1. A1/root66 * [4, 1, -7]
    2. B1/root66
14. 14Determine the angle between the vectors g=[6,1,2] and h=[-5,3,6]

    1. A106.3degree
    2. B6.3degree
15. 15a times b=[a2b3-a3b2, a3b1-a1b3, a1b2-a2b1]

    1. ARichtig
    2. BFalsch
16. 16Determine two vector that are orthogonal to both c=[4,6,-1] and d=[-2,10,11]

    1. A[76,-42,52]
    2. B[38,-21,26]

Beschreibung

Quiz am Ohne Titel, erstellt von Klaus Zhao am 10/05/2017.

Autor

Klaus Zhao

Sprache

English

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