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Problem 41 Easy Difficulty

Find the unit vectors that are parallel to the tangent line to the parabola $ y = x^2 $ at the point $ (2, 4) $.

Answer

There are two unit vectors which are parallel to the tangent line.
They are $$\pm\left(\frac{\mathrm{i}}{\sqrt{17}}+\frac{4 \mathrm{j}}{\sqrt{17}}\right)$$

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Video Transcript

for the given problem, we want to find the two unit vectors that are parallel to the tangent line of the prob. The problem Y equals x squared At the .24. So we're gonna have Y equals X squared. Um and then if we look at the .24, we know that the slope of the line at this point is going to be Um four. So since the slope is for, we know that um the UAE over the X. Component is going to be for, so what this looks like since it's a unit vector is We just need to find the magnitude. So since we have one component that's one and one that's four, we see the magnitude would be route 17. So our unit factors can be won over route 17 Or over Route 17. And then if we wanted a second vector that's parallel, that's a unit vector, we would just look at the negative form of that and it would be the same thing.