If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?

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Question: If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?

Options:

Correct Answer: 10i + 24j

Solution:

Scaling A by 2 gives 2A = 2(5i + 12j) = 10i + 24j.

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?

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.

Vector Scaling – Understanding how to multiply a vector by a scalar to obtain a new vector.