Topic Breakdown of FTCE Physics 6-12 Exam

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FTCE Physics 6-12 Sample Test

1 of 5

The cross product of two vectors, a and b, is equal to c. What is always true of c?

Correct Answer:

c is a vector.

the cross product of two vectors,

a

and

b

, is defined as

c = a \times b

. the result of this operation,

c

, is always a vector. this is a fundamental property of the cross product in vector algebra. the magnitude of

c

is given by

| | a | | | | b | | \sin (θ)

, where

θ

is the angle between

a

and

b

, and

| | a | |

and

| | b | |

are the magnitudes of

a

and

b

respectively. the direction of

c

is perpendicular to both

a

and

b

, following the right-hand rule.

it's important to note that

c

is not necessarily a unit vector. the magnitude of

c

depends on the magnitudes of

a

and

b

, as well as the sine of the angle between them. therefore,

c

will only be a unit vector if

| | a | | | | b | | \sin (θ) = 1

, which is not generally the case for arbitrary vectors

a

and

b

.

additionally,

c

does not bisect the angle between

a

and

b

. instead, as stated earlier,

c

is perpendicular to the plane containing

a

and

b

. the misconception that

c

bisects the angle between

a

and

b

may arise from confusing the cross product with other vector operations, such as the dot product or vector addition.

concerning the magnitude of

c

relative to the sum of

a

and

b

, it is not accurate to claim that

| | c | |

is always greater than

| | a + b | |

. the actual magnitudes depend on the specific vectors and their relative directions. for example, if

a

and

b

are parallel (

θ = 0^{\circ}

θ = 180^{\circ}

), then

\sin (θ) = 0

, making

| | c | | = 0

, regardless of the magnitude of

| | a + b | |

.

in conclusion, the only universally true statement about the vector

c

resulting from the cross product

a \times b

is that

c

is indeed a vector, perpendicular to both

a

and

b

and following the right-hand rule. the other properties, such as being a unit vector or bisecting the angle between

a

and

b

, are not generally true and depend on the specific vectors involved.

FTCE Physics 6-12 Exam Blueprint

Understanding the exact breakdown of the FTCE Physics 6-12 test will help you know what to expect and how to most effectively prepare. The FTCE Physics 6-12 has 75 multiple-choice questions The exam will be broken down into the sections below:

FTCE Physics 6-12 Exam Blueprint
Domain Name	%	Number of Questions
Knowledge of the nature of scientific investigation and instruction in physics	7%	5
Knowledge of the mathematics of physics	8%	6
Knowledge of thermodynamics	10%	8
Knowledge of mechanics	27%	20
Knowledge of waves and optics	18%	14
Knowledge of electricity and magnetism	20%	15
Knowledge of modern physics	10%	8