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Numerade Educator

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Problem 26 Easy Difficulty

Find the vector that has the same direction as $ \langle 6, 2, -3 \rangle $ but has length 4.

Answer

The required vector is $$<\frac{24}{7}, \frac{8}{7}, \frac{-12}{7}>$$

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Video Transcript

doctor we have here, we wanted to Have the same direction as 6-3. We want to have a length of four or magnitude of form. So first thing we want to do is convert it into a unit vector. So we find the magnitude of this and we see it going to be the square root of six birds. So 36 plus nine Class four, which is going to be seven. So now we get that are vector. Our unit vector Will be won over seven times this right here, if you want, you could always multiply that through. But then we're going to want to multiply this by four. So that way it's no longer a unit factor, but a factor with lengths four. So we see this would be 24/7, 12/7. 8/7. Mhm. Mhm. That's right. Here is going to be our final sector.