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.
4(u ⋅ v)

Accepted Answer

Hey, everyone in this problem, we're asked to find 11 multiplied by 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. You have four answer choices. Option A negative 341. Option B 319 option C negative 121 and option D 171. So let's start by writing out what we're trying to find, we're trying to find 11 multiplied by A dot B. OK. So the dot product between A and B. Now let's recall that the dot product, we can write as a one, B, one plus A two B two in this case, because each of our vectors has two components. OK? So we have 11 multiplied by the dot product is gonna be 11 multiplied by A one B one plus A two B two. OK? Now, A one is gonna represent the first component of vector A. OK? So that's gonna be the I component. Similarly, B one is gonna be the I component of vector B and the same thing goes for A two and B two. And so what we're really saying is that the vector A can be written as a one multiplied by I plus A two multiplied by J. And similarly, B could be written as B one multiplied by I plus B two multiplied by J. And that's where those A one, B, one, A two B two S are coming from. OK. So we have everything we need, we just need to substitute in the correct values and simplify this expression. Let me use a square bracket here. All right. So we have a one that's, that I component of A is gonna be nine multiplied by the I component of B which is just one. And then we're gonna add the J component of A negative four multiplied by the J component of B which is five, simplifying inside of our brackets. We get 11 multiplied by nine minus 20. This gives us 11 multiplied by negative which is equal to negative 121. OK. So 11 multiplied by the dot product of A and B is gonna be equal to negative 121 which corresponds with answer choice C. That's it for this one. Thanks everyone for watching. I hope this video helped.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

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