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If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
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Practice Questions
1 question
Q1
If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
10i + 24j
5i + 12j
2i + 3j
7i + 14j
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Scaling A by 2 gives 2A = 2(5i + 12j) = 10i + 24j.
Questions & Step-by-step Solutions
1 item
Q
Q: If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
Solution:
Scaling A by 2 gives 2A = 2(5i + 12j) = 10i + 24j.
Steps: 6
Show Steps
Step 1: Identify the original vector A, which is given as A = 5i + 12j.
Step 2: Understand that scaling a vector by a factor means multiplying each component of the vector by that factor.
Step 3: Since we are scaling by a factor of 2, we will multiply both components of vector A by 2.
Step 4: Multiply the i component: 2 * 5 = 10, so the new i component is 10i.
Step 5: Multiply the j component: 2 * 12 = 24, so the new j component is 24j.
Step 6: Combine the new components to form the new vector: 10i + 24j.
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