Help me with this problem please . Thanks

Let {u1,u2,u3} be an orthonormal basis for an inner product space V. If

dybincka [34]

• ||v|| = 42, which is to say

||v||² = 〈v, v 〉

… = 〈a u₁ + b u₂ + c u₃, a u₁ + b u₂ + c u₃〉

… = a ² 〈u₁, u₁〉 + b ² 〈u₂, u₂〉 + c ² 〈u₃, u₃〉 + 2(ab 〈u₁, u₂〉 + ac 〈u₁, u₃〉 + bc 〈u₂, u₃〉)

… = a ² ||u₁||² + b ² ||u₂||² + c ² ||u₃||²

[since each vector in the basis for V is orthogonal to any other vector in the basis, and 〈x, x〉 = ||x||² for any vector x ]

42² = a ² + b ² + c ²

[since each vector in the basis has unit length]

42 = √(a ² + b ² + c ²)

• v is orthogonal to u₃, so 〈v, u₃〉 = 0. Expanding v gives the relation

〈v, u₃〉 = 〈a u₁ + b u₂ + c u₃, u₃〉

… = a 〈u₁, u₃〉 + b 〈u₂, u₃〉 + c 〈u₃, u₃〉

… = c ||u₃||²

… = c

which gives c = 0, and so

42 = √(a ² + b ²)

• Lastly, 〈v, u₂〉 = -42, which means

〈v, u₂〉 = 〈a u₁ + b u₂ + c u₃, u₂〉

… = a 〈u₁, u₂〉 + b 〈u₂, u₂〉 + c 〈u₃, u₂〉

… = b ||u₂||²

… = b

so that b = -42. Then

42 = √(a ² + (-42)²) → a = 0

So we have a = 0, b = -42, and c = 0.

7 0

3 years ago

For constants a ,b, n, R, Van der waals equation relates the pressure P to the volume V of a fixed quantity of a gas at constant

Dahasolnce [82]

Base on your question where a constant A,B,N, R Van der waals equation relates the pressure P to the volume C at fixed quantity of gas at constant value of Temperature T and the ask is to find the rate of change of volume with the pressure dV/dP and the rate of change is
dP/dV=(P+n2a/V2)/(nb−V)+2n2a/V3

3 0

4 years ago

Ellie has 4 liters of punch for the party she needs to measure out servings in milliliters

9966 [12]

Answer:

4 liters = 4000 milliliters

Ellie have 4000 milliliters of punch

Step-by-step explanation:

Given that Ellie has 4 liters of punch and needs to measure out serving in milliliters.

This is a conversion problem, we need to convert;

4 liters to milliliters

1 liter is equivalent to 1000 milliliters

So,

4 liters will be equivalent to 4 × 1000 milliliters.

Therefore;

4 liters = 4000 milliliters

5 0

3 years ago

The product of two whole numbers is 546 and their sum is 47. What are the two numbers

vodka [1.7K]

The two numbers are 26 and 21. HOPE THIS HELPS!

6 0

3 years ago

A company rents cars The company charges a fee of $12 per day plus $0.30 per mile The company also charges $10 per day for insur

Misha Larkins [42]

Everyday the company charges $12 you for renting the car. So, if you rent the car for 7 days then the cost will be $84. $12 * 7 = $84

And for every mile you drive, you pay $0.30. So, if you drive for 100 miles you will pay $30.

Now we can put this into an equation.

y = 12x + 250(0.30)

5 0

3 years ago