If a vector has magnitude ∣v⃗∣=5|v ⃗ |=5 and direction θ=7π4\theta=\frac{7\pi}{4}, find the vector’s horizontal and vertical components.

vx=3.54v_{x}=3.54 and vy=−3.54v_{y}=-3.54

If a vector has magnitude ∣ v ⃗ ∣ = 5 |v ⃗ |=5 and direction θ = 7 π 4 \theta=\frac{7\pi}{4} , find the vector’s horizontal and vertical components.

Let's see how we can solve this problem. So, here we're told if a vector v has a magnitude of 5, and the direction of 7pi over 4 radians, find the vectors horizontal and vertical components. Okay. Now, whenever I'm solving these types of problems, I always like to start with a graph. So if we draw a simple x y graph over here, we can get a general sense of what our vector looks like. Now I can see that our vector has a magnitude of 5, but the direction is 7pi over 4. Now 7pi over 4 radians is equivalent to about 315 degrees, so you're going to be all the way over here with your vector. So the vector 5, the with a magnitude of 5 is gonna be right about there, and our total angle or direction here is 315 degrees, which is also written as 7pi over 4 radians. So this is what our vector ends up looking like. And if we want to calculate the x component, we can do that with the equation that we're getting. We can also do this for the y component. So what I'm first going to do is find the x component using this equation. We're gonna have the magnitude of v multiplied by the cosine of the angle. Now the magnitude of our vector is 5, and we'll have that times the cosine of 7 pi over 4. Now make sure your calculator is in radian mode when calculating this because we're now dealing with radians. So if you plug this in, you should get a result of approximately 3.54 and that's going to be the x component of our vector. But now let's see if we can find the y component. The y component is going to be the magnitude of our vector multiplied by the sine of the angle. So we're going to have 5 times the sine of 7 pi over 4. Now plugging this into a calculator, your answer should come out to approximately negative 3.54. So this right here is our y component and that is how you can find the horizontal and vertical components of this vector. So hope you found this video helpful. Thanks for watching.

If a vector has magnitude ∣v⃗∣=5|v ⃗ |=5 and direction θ=7π4\theta=\frac{7\pi}{4}, find the vector’s horizontal and vertical components.

vx=3.54v_{x}=3.54 and vy=−3.54v_{y}=-3.54

vx=4.98v_{x}=4.98 and vy=0.479v_{y}=0.479

vx=0.479v_{x}=0.479 and vy=4.98v_{y}=4.98

vx=−3.54v_{x}=-3.54 and vy=3.54v_{y}=3.54

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Multiple Choice

If a vector has magnitude $∣ v ⃗ ∣ = 5$ and direction $θ = \frac{7 π}{4}$ , find the vector’s horizontal and vertical components.

$v sub x equals 4.98$ and $v sub y equals 0.479$

$v sub x equals 0.479$ and $v sub y equals 4.98$

$v_{x} = - 3.54$ and $v sub y equals 3.54$

$v sub x equals 3.54$ and $v_{y} = - 3.54$

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Struggling with Algebra and Trigonometry?

If a vector has magnitude ∣v⃗∣=5|v ⃗ |=5 and direction θ=7π4\(\theta\)=\(\frac{7\pi}{4}\), find the vector’s horizontal and vertical components.

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If a vector has magnitude $∣ v ⃗ ∣ = 5$ and direction $θ = \frac{7 π}{4}$ , find the vector’s horizontal and vertical components.