True or false: If a ⃗ = ⟨ 3 , − 2 ⟩ a ⃗=⟨3,-2⟩ a ⃗ = ⟨ 3 , − 2 ⟩ and b ⃗ b ⃗ b ⃗ has initial point ( − 10 , 5 ) (-10,5) ( − 10 , 5 ) & terminal point ( − 7 , 3 ) (-7,3) ( − 7 , 3 ) , then a ⃗ = b ⃗ a ⃗=b ⃗ a ⃗ = b ⃗ .

Let's give this problem a try. Here we're asked true or false. If vector a is equal to 3 comma negative 2, and vector b has initial point negative 10, 5 and terminal point negative 7, 3, then vector a is equal to vector b. So this is a true or false question, and all we really need to do to solve this problem is figure out what vector b is. Because if it turns out that vector b is the same vector of as vector a, then this is a true statement. Otherwise, the statement is false. And the way that we can figure out what vector b is is using this equation. We're going to have x 2 minus x 1 comma y 2 minus y 1, where these x's and y's refer to the initial and terminal points that we are given. This is always the equation that you can use if you're given 2 points to represent your vector. Now what I'm going to go ahead and do is plug in the values. So we're going to have the terminal point for x, the x two, which I can see is negative 7. And then we're going to have this we're gonna subtract from this the initial point of x, which I can see is negative 10. Now this is going to be comma the difference in the y values, and the terminal y I can see is 3. Then I need to subtract off the initial y, which I can see is 5. So this is the vector that we end up getting. Now let's go ahead and do the math here. So So going to have negative 7 minus negative 10. This is the same thing as negative 7 plus 10, and negative 7 plus 10 is positive 3. This is going to be comma 3 minus 5, which is negative 2, and that's what we get for vector b. And notice how vector b is 3 negative 2, which is the same thing as vector a. So because we got the exact same vector, we would say that vector b is equal to vector a. So this statement is true, and that's how you can go about solving this problem. So hope you found this video helpful. Thanks for watching.