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 = (-1, 7), P₂ = (-7, -7)

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 3 and ends at N where N equals negative four, negative four were asked to express the vector B in terms of I and J. Our answer choices are answer choice A B equals negative seven, I plus 11 J. Answer choice B B equals I plus 19 J. Answer choice C B equals seven I minus J and answer choice DB equals negative I minus 19 J. All right, we recall from previous lessons that 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 and our X sub one and X and Y sub one come from our initial point which is M so negative three is our X sub one and 15 is our Y sibling. And then our X sub two and Y sub sub two come from our terminal point which is N so negative four is our X sub two and negative four is our Y sub two. Now, we just need to plug those in for our vector B. So the vector B equals the quantity of X sub two is negative four minus X sub one is negative three. That's multiplied by I plus the quantity of Y sub two is negative four minus Y sub one is 15 and that's multiplied by J. Now just simplifying what's inside of parentheses. Negative four minus negative three is negative four plus three, which is negative one and negative one multiplied by I is negative I and then negative four minus is negative 19. So we have minus 19 J and that is our solution. We look at our answer choices and this matches with answer choice. D 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 = (-1, 7), P₂ = (-7, -7)

Key Concepts

Vectors

Unit Vectors i and j

Vector Component Calculation

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