In Exercises 13–20, let v be the vector from initial point P₁ to ...

Question

In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.

P₁ = (-8, 6), P₂ = (-2, 3)

Accepted Answer

Welcome back. I am so glad you're here. We are told that A vector B starts at M where M equals negative 12 5 and ends at N where N equals negative express the vector B in terms of I and J. Our answer choices are answer choice A B equals negative 20 I plus six J. Answer choice B B equals four, I plus four J. Answer choice C B equals four, I minus four J and answer choice DB equals 20 I minus six J. All right, we recall from previous lessons that we want to express when we want to express a vector. In terms of I and J, we set that equal to the quantity of X sub two minus X sub one multiplied by I plus the quantity of Y sub two minus Y sub one multiplied by J our X sub one and Y sub one come from the initial point which is M so negative 12 is our X sub one and five is our Y sub one and our X sub two and Y sub two come from our terminal point which is N so negative eight is our X two and one is our Y sub two. Now we just plug those in for our vector B. So B equals the quantity of X sub two is negative eight minus X sub one which is negative 12. And that's multiplied by I then plus the quantity of Y sub two is one minus Y sub one is five and that's multiplied by J. And now we just simplify what's inside of the parentheses. Negative eight minus negative 12 is the same as negative eight plus 12, which is a positive four. So we have four, I and then one minus five is negative four. So minus four J and that is our solution. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-8, 6), P₂ = (-2, 3)

Key Concepts

Vectors

Unit Vectors i and j

Vector Components

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