In Exercises 9–16, let
u = 2i - j, v = 3i + j, and w = i + 4j.

F...

Question

In Exercises 9–16, let
u = 2i - j, v = 3i + j, and w = i + 4j.

Find each specified scalar.
(4u) ⋅ v

Accepted Answer

Hey, everyone in this problem, we're asked to find eight A dot B using the following vectors. We have that A is equal to nine, I minus four J and B is equal to I plus five J. We have four answer choices. Option A 84 option B 72 option C negative 102 and option D negative 88. The question is asking us to take the dot product between eight A and B. So let's just write out our vectors and what we have. OK. So we're gonna have eight multiplied by the vector A which is nine I minus four J dotted with the vector B which is I plus five J. Let's simplify on the left hand side. Let's calculate this vector 88 1st. So this is gonna be 72 I minus 32 J dotted with I plus five J. And now we want to recall the rules for the dot product. If we have a dot product between two vectors, what we wanna do is take the first component of the first vector. So we're gonna take the first component of or the sorry, the I component of the first vector 72. And we're gonna multiply that by the I component of the second vector, which is just one. And then we're gonna add, we're gonna add the J component of the first vector negative multiplied by the J component of the second vector. Yeah. And so we're multiplying light components and then we're adding up all of those components. In this case, we have two components. So we have two terms and then we're multiplying each one together. All right. Simplifying we get 72 minus 160 which is equal to negative 88. OK. And that is an answer we were looking for. What we needed to do was just simplify our eight A vector first and then take the dot product with B just paying attention to which terms correspond with which terms we found that the correct answer is negative 88 which matches with answer choice D. That's it for this one. Thanks everyone for watching. See you in the next video.

In Exercises 9–16, let u = 2i - j, v = 3i + j, and w = i + 4j. Find each specified scalar. (4u) ⋅ v

Key Concepts

Vector Operations

Dot Product

Component Form of Vectors

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