Force Vectors

This quiz contains multiple-choice problems on co-planar forces, Cartesian vectors, the dot and cross products.

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Which statement is correct regarding the force vector F = Ai + Bj + Ck?

As per rectangular components representation, F = Ai + Bj + Ck

As per rectangular components representation, F = Ax + By + Cz

As per rectangular components representation, F = Fx + Fy + Fz

As per rectangular components representation, F = Fi + Fj + Fk

What is the magnitude of a Cartesian vector if its x-, y-, and z-axis components are A, B, and C?

Square root of the squares each A, B and C

Square of the squares each A, B and C

Cube root of the squares each A, B and C

Cube of the squares each A, B and C

If the force vector F’s x-axis component = Z, its y-axis component = X, and its z-axis component = Y, then F is best represented by

Xi + Yj + Zk

Yi + Xj + Zk

Zi + Yj + Xk

Zi + Xj + Yk

What is the mathematical expression for Varignon’s theorem?

M = R x F (F = F1 + F2 + F3 + … vectorially adding all the forces)

|A||B|sinØ

(AxB)xS ≠ Px(QxS)

Px(Q + S) = (PxQ) + (PxS)

What is the dot product of two vectors having a magnitude equal to unity and making an angle of 45°?

0.707 -0.707 1.414 -1.414

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

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

What is distributive law?

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

What is multiplication law?

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

What is k.i?

0 1 -1 ∞

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

1 0 A + B + C -1

A tractor pulls on a 12 m high, upright tree with an attached winch. The tractor is at a distance of 4 m from the tree. If the force applied by the tractor is 2 KN, what is the moment caused by the tree’s roots?

-16.5i+8.51j KNm

-16.5i+6.51j KNm

-16.5i+5.51j KNm

-16.5i+7.51j KNm

Let there be a force along the positive x-axis. Let us also consider three arbitrary points to calculate the moment of the force. If these three points are located along the positive y-axis with varying distances, what will be the direction of the moment caused by the force to the individual points?

Towards the positive x-axis

Towards the positive y-axis

Towards the positive z-axis

Towards the negative z-axis

If A is represented as Ai + Bj + Ck, what is its y-axis component?

Square root of a sum of squares of the three

A units

C units

B units

Which axis is considered positive in the right-hand coordinate system?

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

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