1. What is the sum of squares of the cosine angles made by the force vector with the coordinate axis?
a) 1
b) ½
c) 2
d) 3
Explanation: The sum of the squares of the cosines of the vector will give you the squares of the components in the numerator, and the vector’s magnitude’s square in the denominator. But the numerator sum is equal to the vector’s magnitude’s square. Thus, the answer = 1.
2. What is the x-axis component of the force vector Ai + Bj +Ck with magnitude equal to F?
a) B
b) C
c) Fcosα
d) Fcosβ
Explanation: As we know that the cosα is the ratio of the x-axis component to the magnitude of the vector. Thus the x-axis components is Fcosα, F, the magnitude in the case. Likely if we want to take the y-axis component we would try to do the same with the sine component
3. We can add the force vectors directly. But with dividing each by it’s magnitude first.
a) True
b) False
Explanation: False, because if you will divide the magnitude of the vector to itself than the resulting would be the unit vector. Which is just giving you the direction of the vector, not the vector itself. This means unit vector has direction same as it’s respective vector but having a magnitude equal to one.
4. For a vector F, Fcosβ is equal to zero. What does this refer?
a) X-axis component is zero
b) Y-axis component is zero
c) Z-axis component is zero
d) β = 180˚
Explanation: As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus y-axis component is zero, or β = 90˚. And thus if the angle is giving component to be zero this means the vector in that particular axis is perpendicular to that axis.
5. Which statement is correct about the vector F?
a) F= Fcos β + Fcos α + Fcosγ
b) F= Fsin β + Fcos α + Fcosγ
c) F= Fcos β + Fsin α + Fcosγ
d) F= Fcos β + Fcos α + Fsinγ
Explanation: As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus, is the magnitude of the vector is F, the F= Fcos β + Fcos α + Fcosγ. Which means the force is the resultant of all its axis’ components.
6. Which is true?
a) ∑F = ∑Fx + ∑Fy + ∑Fz
b) ∑F = -(∑Fx + ∑Fy + ∑Fz)
c) ∑F = ∑Fxi + ∑Fyj + ∑Fzk
d) ∑F = -(∑Fxi+ ∑Fyj + ∑Fzk)
Explanation: The total of two or more forces is equal to the sum of their respective axis’s components. That is the resultant adds up all the components of the forces in their respective axis, whether it may be x, y or z axis
7. 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.
a) 60˚
b) 120˚
c) 45˚
d) 90˚
Explanation: When you will resolve the vector in its x, y and z-axis components, you will get an equation containing cosα. After getting the α correctly, you need to directly put that value in the previous equation of components. α = 60˚. As 120˚ will give a negative component. Just try to resolve the vector in its components.
8. For two vectors A and B, what is A.B (if they have angle α between them)?
a) |A||B| cosα
b) |A||B|
c) √(|A||B|) cosα
d) |A||B| sinα
Explanation: The dot product of the two vectors is always the product of the magnitudes of the two forces and the cosine of the angle between them. We need to consider the triangle and then accordingly apply the trigonometry. This is one of the ways of resolving the components
9. Which statement is right?
a) Communitive law: A.B =B.A
b) Multiplicative law: a(A.B) = Ax(aB)
c) Multiplicative law: A.(B+D) = (A.B) + (A.D)
d) Communitive law: a(A.B) = A.(aB)
Explanation: For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB)
10. What is Distributive law?
a) A.B =B.A
b) a(A.B) = A.(aB)
c) A.(B+D) = (A.B) + (A.D)
d) a(A.B) = AxB
Explanation: For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).