Force Vectors topics include: Coplanar forces, cartesian vectors, dot and cross product. A force vector is a representation of a force that has both magnitude and direction. A force vector has three components: magnitude, orientation, and sense. The magnitude of a vector is specified by a positive number and a unit. The orientation of a vector is specified by the relationship between the vector and given reference lines and/or planes.  Forces can cause motion or act to keep objects at rest. Forces acting on any object change its movement. The change depends on the strength and directions of... Show more

Force Vectors topics include: Coplanar forces, cartesian vectors, dot and cross product.

A force vector is a representation of a force that has both magnitude and direction. A force vector has three components: magnitude, orientation, and sense. The magnitude of a vector is specified by a positive number and a unit. The orientation of a vector is specified by the relationship between the vector and given reference lines and/or planes. 

Forces can cause motion or act to keep objects at rest. Forces acting on any object change its movement. The change depends on the strength and directions of forces and on the way the object moved. 
The formula for solving problems about force is F=ma, where m is the mass of the particle. If a particle is resting in equilibrium then the resultant of all the forces acting on it is zero. 

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Engineering Mechanics Practice Test: Force Vectors

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25 Questions

1. Force vector R is having a______________

Length of R and a specific directionLength of RLength of magnitude equal to square root of R and a specific directionA specific direction

2. If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by?

Zi + Xj + YkYi + Xj + ZkXi + Yj + ZkZi + Yj + Xk

3. Which is true for two vector A = A1i + A2j + A3k and B = B1i + B2j + B3k?

AxB = A1B1 + A2B2 + A3B3A.B = A1B2 + A2B3 + A3B1A.B = A1B1 + A2B2 + A3B3AxB = A1B2 + A2B3 + A3B1

4. For a vector F, Fcosβ is equal to zero. What does this refer?

β = 180˚X-axis component is zeroY-axis component is zeroZ-axis component is zero

5. For two vectors A and B, what is A.B (if they have angle α between them)?

|A||B| sinα|A||B||A||B| cosα√(|A||B|) cosα

6. Two vectors emerging from a point are always in a single plane.

MaybeDon't KnowFalseTrue

7. The value cos-1(-3/7) + cos-1(2/7) + cos-1(6/7) is ____________

188.4˚273.4˚215.4˚219.4˚

8. Determine the magnitude of the projection of the vector force F = 100N, onto u axis, from the figure given below.

70.7N96.6N100N60N

9. What is multiplication law?

A.B =B.Aa(A.B) = A.(aB)A.(B+D) = (A.B) + (A.D)a(A.B) = AxB

10. What is the magnitude of the Cartesian vector having the x, y and z axis components to be A, B and C?

Square root of the squares each A, B and CCube of the squares each A, B and CSquare of the squares each A, B and CCube root of the squares each A, B and C

11. What is {(i.i) + (-i.j) + (-k.k) + (k.i)}.(Ai +Bj + Cz)?

-110A + B + C

12. Mathematically, for two vectors A and B of any magnitude, the cross product of both, i.e. AxB = given by:

|A||B||A||B|cosØ|A||B|sin(180°+Ø)|A||B|sinØ

13. Which statement is right?

Multiplicative law: A.(B+D) = (A.B) + (A.D)Multiplicative law: a(A.B) = Ax(aB)Communitive law: a(A.B) = A.(aB)Communitive law: A.B =B.A

14. What is Distributive law?

a(A.B) = AxBa(A.B) = A.(aB)A.(B+D) = (A.B) + (A.D)A.B =B.A

15. Which statement is right for force vector F = Ai + Bj + Ck?

In rectangular components representation of any vector we have vector F = Fx + Fy + FzIn rectangular components representation of any vector we have vector F = Ai + Bj + CkIn rectangular components representation of any vector we have vector F = Ax + By + CzIn rectangular components representation of any vector we have vector F = Fi + Fj + Fk

16. Find the angle α, for the vector making an angle by y and z axis as 60˚ and 45˚ respectively. It makes an angle of α with x-axis. The magnitude of the force is 200N.

45˚60˚120˚90˚

17. We can add the force vectors directly. But with dividing each by it’s magnitude first.

TrueFalseMaybeDon't Know

18. What is the sum of squares of the cosine angles made by the force vector with the coordinate axis?

3½12

19. The magnitude of the resultant of the two vectors is always_____________

Axis we choose to calculate the magnitudeGreater than one of the vector’s magnitudeSmaller than one of the vector’s magnitudeDepends on the angle between them

20. What is the difference between a position vector and unit vector?

Position vector has some magnitude and direction, while the unit vector has magnitude = 1 and a specified directionPosition vector has magnitude = 0 and direction, while unit vector has magnitude = 0 and no directionPosition vector has some magnitude and direction, while the unit vector has magnitude = 0 and no directionPosition vector has magnitude = 1 and direction, while the unit vector has magnitude = 0 and no direction

21. The coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?

-557i + 482j + 139k N557i – 482j – 139k N-557i + 482j – 139k N-557i – 482j + 139k N

22. Express the vector in the Cartesian Form, if the angle made by it with y and z axis is 60˚ and 45˚ respectively. Also, it makes an angle of α with the x-axis. The magnitude of the force is 200N.

100i + 100j – 141.4k N100i – 100j – 141.4k N100i + 100j + 141.4k N100i – 100j + 141.4k N

23. In right handed coordinate system which axis is considered to be positive?

The thumb is y-axis, fingers curled from x-axis to z-axisThe thumb is x-axis, fingers curled from z-axis to y-axisThe thumb is z-axis, fingers curled from y-axis to x-axisThe thumb is z-axis, fingers curled from x-axis to y-axis

24. If two equal vector forces are mutually perpendicular then the resultant force is acting at which angle as compared to one of the vector?

45 degree180 degree90 degree0 degree

25. What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at the origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?

It is either in the 1st quadrant or in the 3rd quadrantIt is either in the 1st quadrant or in the 4th quadrantIt is either in the 1st quadrant or in the 2nd quadrantOnly in the 1st quadrant