Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.

Question

- 2u + 4v

Accepted Answer

Welcome back everyone. In this problem, considering the vectors A equals negative 611 and B equals 13 7, we want to determine the vector negative eight A plus 11. B. For our answer choices A says our result is 191 11. B says it's 191 negative 11 C says it's 143 11. And B says it's 191 88. No. In this problem, we are taking our vectors A and B and we're multiplying A by negative eight B by 11. And then adding our results. Now, in the first instance, we are multiplying a scalar by a vector and to multiply a scalar by a vector, it means that we multiply all the components of the vector by that value. So negative eight A is going to be negative eight, multiplied by the vector negative 611 and 11 B is going to be 11 multiplied by 13 7. So that means we're gonna multiply negative six by negative eight. OK, and negative eight by 11 in our first term. Well, in our second term, we're going to multiply 11 by 13 and 11 by seven. No, negative eight multiplied by negative six. That's positive 48 negative eight multiplied by 11 equals negative 88 while 11 multiplied by 13, uh that would be equal to 156. Ok. Oh, sorry. No, that would be equal to 143. My bad while 11 multiplied by seven equals 77. No, we're not done yet because no, we still need to combine our vectors here. Notice that we have two vectors. And if we're adding vectors, that means we add their respective components, we're going to add their X components and their Y components. So that means no, we're going to have 48 plus 143 for our X component and negative 88 plus 77 for our Y component ne sorry, 48 plus 143 equals 191 while negative 88 plus 77 equals negative 11. So our final result, our final vector for negative eight A plus 11 B is 191 negative 11. If we look back in our answer choices, the correct choice is answer choice. B thanks a lot for watching everyone. I hope this video helped.

Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.
- 2u + 4v

Key Concepts

Vector Addition and Scalar Multiplication

Component-wise Operations

Notation and Vector Representation

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