right-handed

Vector algebra, as we are going to use it, is based on a _____ coordinate system.

coordinate direction angles

The symbols, (alpha), (beta), and (gamma) designate the _____ of a 3-D Cartesian vector.

angles (alpha, beta, gamma)

If you know only Ua, you can determine the _____ of A uniquely.

all three angles are arbitrarily picked, unit vectors are uniquely picked.

For a force vector, the following parameters are randomly generated. The magnitude is 0.9 N, alpha=30, beta=70, gamma=100. What is wrong with this 3-D vector?

it always points in the direction of positive x-axis

What is not true about an unit vector?

30i+30j+30k

If F={10i+10j+10k} N and G={20i+20j+20k} N, then F+G={_____} N

coordinates of Q minus coordinates of P

The position vector r_pq is obtained by

F(U)

A force of magnitude F, directed along a unit vector, U, is given by F=_____

r_pq=-r_qp

P and Q are two points in 3-D space. How are the position vectors r_pq and r_qp related?

meters

If F and r are force and position vectors, respectively, in SI units, what are the units of the expression (r*(~F~/F))?

{-3i-3j-3k}m

use P-Q

Two points in 3-D space have coordinates of P(1,2,3) and Q(4,5,6) meters. The position vector ~r_qp~ is given by _____

F(~r_pq~/r_pq)

A force vector, ~F~, directed along a line defined by PQ is given by ______

PQcos(theta)

The dot product of two vectors P and Q is defined as _____

scalar

The dot product of two vectors results in a _____ quantity

perpendicular

If a dot product of two non-zero vectors is 0, then the two vectors must be ______ to each other?

parallel (pointing in the opposite direction)

If a dot product of two non-zero vectors equals -1, then the vectors must be _____ to each other

the sum of two vectors

The dot product can be used to find all of the following except _____

{-10+10+12} m^2 = 12 m^2

Find the dot product of the two vectors P and Q:

P={5i+2j+3k} m

Q={-2i+5j+4k} m

P={5i+2j+3k} m

Q={-2i+5j+4k} m

zero

When a particle is in equilibrium, the sum of forces acting on it equals _____.

T1=T2

For a frictionless pulley and cable, tensions in the cable (T1 and T2) are related as _____.

**choose drawing with 4 ropes**

There are more unknowns than equations

Assuming you know the geometry of the ropes, in which system can you NOT determine forces in the cables? Why?

A scalar is any positive or negative physical quantity that can be completely specified by its magnitude. Examples are length, mass, and time.

Define scalar

A vector is any physical quantity that requires both a magnitude and direction for its complete description. Examples are force, position, and moment.

A= (Axi+Ayj+Azk) m

Define vector

The resultant vector A+B is determined by the closing side of triangle by placing the vectors A and B “tip-to-tail”

Define the triangle rule for adding vectors

Express each force as a Cartesian vector and add the i, j ,k componets of all the forces in the system.

Fr=(sum)F=(sum)Fxi+(sum)Fyj+(sum)Fzk

Fr=(sum)F=(sum)Fxi+(sum)Fyj+(sum)Fzk

Define the concurrent force system

A detailed drawing of an object in which the object is isolated (i.e. no supports) from its surroundings and all external forces acting on the body are shown

Define a free body diagram

The resultant vector is unaffected by the order of additive terms.

R=A+B=B+A

Define parallelogram rule for adding vectors

C=sqrt(A^2+B^2-2ABcos(c))

Define cosines

A position vector locates one point in space relative to another.

Define position vector

Magnitude=0

Coordinate axes= cos(alpha)i+cos(beta)j+cos(gamma)k

cos(-0.456)i+cos(-0.684)j+cos(0.569)k

What is the magnitude of the given unit vector, U? What are the angles relative to the coordinate axes?

u=-0.456i-0.684j+0.569k

If the angles of a unit vector are as follows, what is gamma?

alpha=120

beta=60

A body is said to be in force equilibrium when the resultant of all the forces acting on a body is zero.

Fx=0, Fy=0, Fz=0

Define force equilibrium in 2D/3D

straight line colinear with the force vector, F

_ _ _ ______ _ _ _

Define the line of action of a force vector

U1=1

U2=1

U2=1

unit vector is a vector whose magnitude is always 1

Find the magnitudes of the following unit vectors:

U1=-0.8329i-942j+34k

U2= 23.3/34i-3452/35654j+567/567k

True

True or False

A particle has a mass but negligible shape/size.

False

True or False

If a vector, A, has the same magnitude as vector, B, then êa=êb.

False

True or False

A rigid body has a mass but negligible shape/size.

False

True or False

If vector, A, is perpendicular to vector, B, then AxB=0.

False

True or False

The subject called statics studies only body which are at rest.

A/sin(a)=B/sin(b)=C/sin(c)

Defines sines