Let u = 〈-2, 1〉, v = 〈3, 4〉,...

Question

Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.

(3u) • v

Accepted Answer

Welcome back everyone. In this problem for the vectors U equals negative 10 6 and V equals 1219. We want to find the value of the expression HV. For our answer choices A says it's 49 B negative 48 C negative 1872 and D 1872. No. Here in this expression, what it's telling us is that we're multiplying the vector U by the scalar eight and then finding the result or the dot product of that result. And V now when we multiply our vector by a scaler, it means we multiply all the components of that vector by that Scaler term. So eight Uau let's first find eight and then dot the result with V. So eight means that we're multiplying negative 10 6 by eight. And that means that we're going to multiply negative 10 by eight. OK? And you get to attend by it and we're going to multiply six by eight. Now negative 10, multiplied by eight equals negative 80 and six multiplied by eight equals 48. So eight is negative 8048. Now we are going to take that and find the dot product of that result with V and to find the dot product of two vectors, we multiply their respective components. In this case, we are going to multiply the X components respectively and the Y components respectively. So that means then for our vector A U dot V is going to be equal to negative 8048 dot 1219. Now multiplying the components are multiplying the respective components that's going to give us negative 80 multiplied by 12 plus 48 multiplied by 19. OK? Because we multiply the respective components and then add them together. No negative 80 multiplied by 12 equals negative 960 48 multiplied by 19 equals 912 negative 960 plus 912 equals negative 48. So the dot product of eight U and V is negative 48. When we look back on our answer choices that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.
(3u) • v

Key Concepts

Vector Scalar Multiplication

Dot Product of Vectors

Properties of Dot Product with Scalar Multiplication

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