In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each...

Question

In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar.

w - v

Accepted Answer

Hey, everyone in this problem, we're asked to find five A minus two B using the vectors A equals I minus 11 J and B is equal to negative three, I plus nine J. We're given four answer choices. Option A negative 14, I minus 82 J. Option B 11, I minus 73 J. Option C negative four, I minus 28 J and option D negative four, I plus 28 J. We're gonna start by rewriting the expression we're trying to find. So we have five A minus two B. We're just gonna go ahead and substitute in the values of our vectors. So this is gonna be equal to five multiplied by the vector I minus 11 J minus two, multiplied by the vector negative three. All right. Sorry. There we go negative three I plus nine J. All right. Now, when we're multiplying vectors by these scalar multiples, like we're multiplying A by five, we're multiplying B by two when we're doing that multiplication, OK. We want that scalar multiple to apply to each component of our vector. And so we're gonna multiply just like that. We would anything else we want to take this factor of five and apply it and expand these brackets. So if we do that to the first vector, we have five multiplied by I which gives us five I and then we have five multiplied by negative 11 J which gives us minus 55 J. Now we move to the second half of our expression and we're gonna do the same thing. We have this factor of negative too. We're gonna apply it to negative three. I so negative two multiplied by negative three. I gives us positive six. All right. And then we have negative two multiplied by nine J which gives us negative 18 J. So now we have all of these components that we've expanded and we're adding and subtracting. And when you add and subtract vectors, what you're gonna do is just add and subtract the corresponding components. OK? So we wanna add like terms here. So we're gonna take our I terms first. We have five I and we have plus six I. It's gonna give us 11. All right. And then we're gonna take our J terms. We have negative 55 J minus 18 J. That's gonna give us minus 73 J. And so the final value of our expression, the vector value is gonna be 11 I minus 73 J which corresponds with answer choice. B thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar.
w - v

Key Concepts

Vector Representation in Component Form

Vector Subtraction

Geometric Interpretation of Vector Operations

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