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konstantin123 [22]
3 years ago
15

Let vector a = 3i + j - k. Find the vector b in the direction of vector a such that |b| = 5

Mathematics
1 answer:
Serjik [45]3 years ago
3 0

Answer:

5i +(5/3)j - (5/3)k

Step-by-step explanation:

Vector b is in the same direction as vector a, so it is a scalar multiple of a.

b = ca for some positive real number c.

b = c(3i + j - k) = 3ci + cj - ck

|b| = sqrt[(3c)^2 + c^2 - c^2] = sqrt(9c^2) = 3c

If |b| = 5, then 3c = 5 and c = 5/3

That makes b = (5/3)(3i + j - k) = 5i +(5/3)j - (5/3)k

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Determine if they are congruent. State how they are.
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2 years ago
What is the prime factorization of 240? Question options: 24 · 3 · 7 23 · 3 · 5 24 · 5 23 · 5 · 7 24 · 3 · 5
timama [110]

The prime factorization of 240 is 2^{4} . 3 . 5 ⇒ last answer

Step-by-step explanation:

Prime number is the number that has only 2 factors 1 and itself

{2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , ............}

In prime factorization we use only the prime numbers

Ex: The factors of 15 are 1 , 3 , 5 , 15,

      Then the prime factors of 15 are 3 and 5 only because they are

       prime numbers

So to find the prime factors of a number do that

1. Factorize the number by divide it using prime numbers only

2. Write the number as a product of its prime factors

∵ 240 divisible by first prime number 2

∴ 240 ÷ 2 = 120

∵ 120 ÷ 2 = 60

∵ 60 ÷ 2 = 30

∵ 30 ÷ 2 = 15

- We divided the number by 2 for 4 times

∴ 2^{4} is a prime factor of 240

∵ 15 is divisible by prime number 3

∴ 15 ÷ 3 = 5

∴ 3 is a prime factor of 240

∵ 5 is divisible by prime number 5

∴ 5 ÷ 5 = 1

∴ 5 is a prime factor of 240

∴ The prime factors of 240 are 2^{4} , 3 , 5

The prime factorization of 240 is 2^{4} . 3 . 5

Learn more:

You can learn more about factors in brainly.com/question/5194236

#LearnwithBrainly

7 0
3 years ago
Shelly is 3 years older than Michelle. 4 years ago the sum of their ages was 67. find the age of each person now
Murljashka [212]
If Shelly is 3 years older than Michael and There 67. Michael is 64 and Shelly is 67. Or Michael is 67 and Shelly is 70.

Hope I helped. Have a wonderful day
3 0
3 years ago
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