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 = (-3, 4), P₂ = (6, 4)

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 7 and ends at N where N equals 14, 8 express the vector B in terms of I and J. Our answer choices are answer choice A B equals I plus J. Answer choice B B equals four, I minus J. Answer choice C B equals negative 24 I plus J and answer choice DB equals four I plus J. All right, we recall from previous lessons that in order to express a vector, in terms of I and J, we set it 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. And now our X sub one and Y sub one are going to be with our initial point which is M so negative 10 is our X sub one and seven is our Y sub one and then our X sub two and our Y sub two will be with the terminal point N so 14 is our X sub two and eight is our Y sub two. Now, we just need to plug those in for our vector B. So we have the quantity of X sub two is 14 minus X sub one is negative 10. And that is multiplied by I plus. The quantity of our Y sub two is eight minus our Y sub one is seven and that is multiplied by J. Now, just simplifying what's in parentheses, 14 minus negative 10 is 14 plus 10, which is 24. So we have 24 I plus eight minus seven is one. So one J is just J and there's our solution. We look at our answer choices and this matches with answer choice. A 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 = (-3, 4), P₂ = (6, 4)

Key Concepts

Vectors

Unit Vectors i and j

Vector Subtraction

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