Precisely! Scalar multiplication is very simple. We just have to multiply the x- and the y-components ($$3$$ and $$-2$$ respectively) by $$5$$, that's it!
If $$\vec{A} = \hat{i} - \hat{j}$$, $$\vec{B} = - 2 \hat{i} + 3 \hat{j}$$ and $$\vec{C} = 2 \hat{i} + \hat{j}$$, what is $$3 \vec{A} - 2 \vec{B} + 4 \vec{C}$$?
• $$15 \hat{i} - 5 \hat{j}$$
• $$9 \hat{i} + 7 \hat{j}$$
• $$-9 \hat{i} - 7 \hat{j}$$
• $$12 \hat{i} - 5 \hat{j}$$
The passage introduces scalar multiplication and then presents a vector problem asking for the result of a linear combination of vectors. It also provides multiple-choice answers.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Precisely! Scalar multiplication is very simple. We just have to multiply the x- and the y-components ($$3$$ and $$-2$$ respectively) by $$5$$, that's it!
If $$\vec{A} = \hat{i} - \hat{j}$$, $$\vec{B} = - 2 \hat{i} + 3 \hat{j}$$ and $$\vec{C} = 2 \hat{i} + \hat{j}$$, what is $$3 \vec{A} - 2 \vec{B} + 4 \vec{C}$$?
• $$15 \hat{i} - 5 \hat{j}$$
• $$9 \hat{i} + 7 \hat{j}$$
• $$-9 \hat{i} - 7 \hat{j}$$
• $$12 \hat{i} - 5 \hat{j}$$
user
The passage introduces scalar multiplication and then presents a vector problem asking for the result of a linear combination of vectors. It also provides multiple-choice answers.

TYPE: SINGLE_QUESTION_WITH_ANSWER