If vector v ⃗ v ⃗ v ⃗ has initial point ( − 1 , 2 ) (-1,2) ( − 1 , 2 ) and terminal point ( 9 , 5 ) (9,5) ( 9 , 5 ) , calculate the magnitude ∣ v ⃗ ∣ |v ⃗ | ∣ v ⃗∣ .

Let's see how we can solve this problem. So we are told if vector v has initial point negative 12, and terminal point 95, calculate the magnitude of this vector. Now to solve this problem, I noticed that we're given points for our vector. So what we first need to do is figure out what the vector is going to be in component form, and I can do that by using this equation. It's going to be the final x minus the initial x, and then comma the final y minus the initial y. So we can use this equation to find our vector in component form. Now what I can see here is that we have our final x, which is 9, and what I can do is I can take 9, and I can subtract off the initial x, which is negative one. So we're going to have 9 minuteus negative one for the x's. Now for the y's, what I can see here is that we have our final y, which is 5, and then we can subtract this 5 here from our initial y, and you can see that the initial y is 2. So we're going to have 5 minus 2, and this right here was going to be the vector. Now 9 minus negative one, that's the same thing as 9+1. So So we're going to have 9+1, which is 10, comma 5 minuteus 2, which is 3. So this is what our vector ends up becoming for component format. It's going to be 10, comma, 3. Now from here, what I can do is find the magnitude of this vector by using the pythagorean theorem. And the pythagorean theorem for vectors looks like this is going to be the square root of the x component squared plus the y component squared. Now we can see down here that the x component is this 10. So we're going to have 10 squared plus this y component, which we can see here is 3. So we're gonna have 3 squared. So we have the square root of 10 squared plus 3 squared. 10 squared is a 100. 3 squared is 9, and a 100+9 is 109. Now it turns out the 109 here, this is a prime number. We can't break this down any farther than what it is. So we can't simplify this radical, so this right here would be the magnitude of our vector in simplified form, and this would also be the solution to the problem. So hope you found this video helpful. Thanks for watching.

8. Vectors

Vectors in Component Form

Trigonometry

8. Vectors

Vectors in Component Form

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Multiple Choice

If vector $v ⃗$ has initial point $(-1,2)$ and terminal point $(9,5)$ , calculate the magnitude $|v ⃗ |$ .

$2√29$

$\surd109$

$\surd73$

$\surd113$

Verified step by step guidance

Identify the initial point $(-1, 2)$ and the terminal point $(9, 5)$ of the vector $\vec{v}$.

Calculate the components of the vector $\vec{v}$ by subtracting the coordinates of the initial point from the coordinates of the terminal point: $v_x = 9 - (-1)$ and $v_y = 5 - 2$.

Simplify the components: $v_x = 9 + 1 = 10$ and $v_y = 5 - 2 = 3$.

Use the formula for the magnitude of a vector $\vec{v} = (v_x, v_y)$, which is $|\vec{v}| = \sqrt{v_x^2 + v_y^2}$.

Substitute the components into the formula: $|\vec{v}| = \sqrt{10^2 + 3^2}$ and simplify to find the magnitude.

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Struggling with Trigonometry?

If vector v⃗v ⃗ v⃗ has initial point (−1,2)(-1,2)(−1,2) and terminal point (9,5)(9,5)(9,5), calculate the magnitude ∣v⃗∣|v ⃗ |∣v⃗∣.

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Vectors in Component Form practice set

If vector $v ⃗$ has initial point $(-1,2)$ and terminal point $(9,5)$ , calculate the magnitude $|v ⃗ |$ .