Let v be the vector from initial point P₁ to terminal point P₂...

Question

Let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.

P₁ = (2, -5), P₂ = (-6, 6)

Accepted Answer

Welcome back, everyone. A vector starts at P one and ends at P two express the vector A in terms of I and J where P one equals negative 34 and P two equals five, negative two A says it's eight, I minus six JB eight, I plus six JC six, I minus eight J and D six I eight J. Now let's first try to visualize what the vector A may look like to get a better understanding of our problem. OK. So let's imagine here that these are our, our axis. OK? And we know that P one is at negative 34. OK. So it's gonna be in the second quadrant probably somewhere here while P two is at five, negative two. So it's gonna be in the fourth quadrant probably somewhere here. OK? And now we know that our vector A starts at P one and ends at P two. And we're trying to find a in terms of I and J. Now I and J just represent the change in X and Y coordinates for our vector A, its components. So we know then that vector A is going to be equal to the change in X for the I component plus the change in Y for the J component. Now, what do we know about the change in X? Well notice here, OK that we're going to the right, OK. And for this change, we go from negative 3 to 5. OK. So our change in X is going to be the difference between five and a negative three which equals eight. On the other hand, for our change in Y OK, we're going from four all the way down to negative two. OK? You probably write that on the other side just to visualize it a bit better here. So no notice that that change is going to be negative two minus four which equals negative six. Therefore, this tells us that A is going to be equal to eight I minus six J. Therefore, it is the correct answer. Thanks for watching everyone. I hope this video helped.

Let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.

P₁ = (2, -5), P₂ = (-6, 6)

Key Concepts

Vectors

Unit Vectors i and j

Vector Subtraction

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