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ankoles [38]
3 years ago
12

The following statement is either true​ (in all​ cases) or false​ (for at least one​ example). If​ false, construct a specific e

xample to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is​ true, give a justification. If v1 and v2 are in set of real numbers R Superscript 4 and v2 is not a scalar multiple of v1​, then ​{v1​,v2​} is linearly independent. Choose the correct answer below. A. The statement is false. The vector v1 could be a scalar multiple of vector v2. B. The statement is false. The vector v1 could be the zero vector. C. The statement is true. A set of vectors is linearly independent if and only if none of the vectors are a scalar multiple of another vector. D. The statement is false. The vector v1 could be equal to the vector v2.
Physics
1 answer:
Jlenok [28]3 years ago
3 0

Answer:

  • B. The statement is false. The vector v1 could be the zero vector.

Explanation:

Two vectors \vec{v}_1 and \vec{v}_2 are linearly independent if the equation

\alpha_1 \vec{v}_1 + \alpha_2 \vec{v}_2 = \vec{0}

where \alpha_1 and \alpha_2 are scalars, has only one solution:

\alpha_1 = \alpha_2 = 0.

If there is more than one solution, we say that the vector are linearly dependent.

<h3>Why the answer is B. :</h3>

if \vec{v}_1 = 0 then, \alpha_1 could have any value of the scalar group, as for any scalar \alpha

\alpha * \vec{0} = \vec{0}

So, we get that there is more than one solution.

So, a particular counterexample is:

\vec{v}_1  = (0,0,0,0)

\vec{v}_2 = (1,0,0,0)

as \vec{v}_2 is not an scalar multiple of \vec{v}_2, and the equation

\alpha_1 \vec{v}_1 + \alpha_2 \vec{v}_2 = \vec{0}

has as solution

\alpha_1 = 2

\alpha_2 = 0

as we can see

2 (0,0,0,0) + 0 (1,0,0,0) = \vec{0}

(2* 0,2 *0,2*0,2*0) +  (0*1,0*0,0*0,0*0) = \vec{0}

(0,0,0,0) +  (0,0,0,0) = \vec{0}

(0+0,0+0,0+0,0+0) = \vec{0}

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You drive on Interstate 10 from San Antonio to Houston, half the time at 72 km/h and the other half at 98 km/h. On the way back
zimovet [89]

Answer: a. 85km/hr b.82.3km/hr

c. 84km/hr

Explanation: first let take the total time from San Antonio to Houston to be 2hr.

Half time 1hr was covered with speed of 72km/hr

Distance = speed*time=72km/hr *1hr

=72km

So too with the second half of 1hr covered with speed of 98km/hr

Distance = 98km

Total distance from Houston to San Antonio is 98+72 =170km

a. Average speed from San Antonio to Houston is

S1 =170/2

=85km/hr

b.half distance from Houston to San Antonio which is 170km/2

= 85km was covered with speed of 72km/hr first half, so time

t = dist/speed

t = 85/72 = 1hr 12 mins

Remaining 85 km covered with a speed of 98km/hr

Time = 85/98 = 0.88*60min

= 52 mins

Total time = 1hr +12mins +52mins

=2hr4mins= 124/60 hr

So average speed = distance/time

=170/124/60

Using reciprocal law

Average speed S2= 170*60/124

= 82.3km/hr

C. Average speed to and fro(entire tripe)

= (85+82.3)/2

=84km/hr

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2 years ago
Combine these three velocity vectors into a resultant: 3.0 m/s north, 4.0 m/s east 1.0 m/s west. Identify the resultant vector
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Answer:

The resultant vector is 1 m/s

Explanation:

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How much force is required to accelerate a 2kg mass at 3 m/s2? answer key?
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A Van de Graaff generator is one of the original particle accelerators and can be used to accelerate charged particles like prot
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Answer:

595391.482946 m/s

3.21875\times 10^{6}

Explanation:

E = Energy = 1.85 keV

I = Current = 5.15 mA

e = Charge of electron = 1.6\times 10^{-19}\ C

t = Time taken = 1 second

m = Mass of proton = 1.67\times 10^{-27}\ kg

Velocity of proton is given by

v=\sqrt{\dfrac{2E}{m}}\\\Rightarrow v=\sqrt{\dfrac{2\times 1.85\times 10^3\times 1.6\times 10^{-19}}{1.67\times 10^{-27}}}\\\Rightarrow v=595391.482946\ m/s

The speed of the proton is 595391.482946 m/s

Current is given by

I=\dfrac{\Delta Q}{t}\\\Rightarrow \Delta Q=It\\\Rightarrow \Delta Q=5.15\times 10^{-3}\times (1\ sec)\\\Rightarrow Q=5.15\times 10^{-3}\ C

Number of protons is

n=\dfrac{Q}{e}\\\Rightarrow n=\dfrac{5.15\times 10^{-3}}{1.6\times 10^{-19}}\\\Rightarrow n=3.21875\times 10^{6}\ protons

The number of protons is 3.21875\times 10^{6}

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It is most accurate to say that body mass index (BMI) provides information about an individual's height-weight ratio. The correct answer is B.
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