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Find the component form of v = u + 2w, where u = 2i- j and w = i + 2j.

User Mattsilver
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2 Answers

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9 votes

Final answer:

The component form of vector v is determined by multiplying vector w by 2 and then adding it to vector u component-wise, resulting in the component form 4i + 3j.

Step-by-step explanation:

To find the component form of a vector v where v = u + 2w, and given u = 2i - j and w = i + 2j, we need to perform vector addition. We multiply vector w by 2 and then add it to vector u component-wise.

The resulting vector, in terms of its components, is calculated as follows:

  1. First, multiply w by 2: 2w = 2(i + 2j) = 2i + 4j.
  2. Then add this to u: v = u + 2w = (2i - j) + (2i + 4j).
  3. Combine the i and j components: v = (2+2)i + (-1+4)j = 4i + 3j.

Therefore, the component form of vector v is 4i + 3j.

User Niklasbec
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23 votes
23 votes

We have the next vectors:

u = 2i- j

w = i +2j

Now, we need to find v = u + 2w:

Where 2w:

2(w = i +2j) = 2w = 2i+4j

Then, u+2w:

(2i- j) + 2i+4j = 2i-j+2i + 4j = 4i + 3j

Hence, the answer is v= 4i + 3j

User Skodsgn
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3.0k points