Find unit vectors that satisfy the given conditions below.
The unit vector in the same direction as .
The unit vector in the opposite direction of .
The unit vector that has the same direction as the vector from the point to the point
.
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Ask by Boyd Cole. in the United States

Mar 26,2025

Question

Find unit vectors that satisfy the given conditions below.
The unit vector in the same direction as .
The unit vector in the opposite direction of .
The unit vector that has the same direction as the vector from the point to the point
.
Question Help: Video 1 Video 2
Submit Question

Ask by Boyd Cole. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

1. For the unit vector in the same direction as $$ \langle 2,7\rangle $$:

- Compute the magnitude:
     $$
     \|\langle 2,7\rangle\| = \sqrt{2^2 + 7^2} = \sqrt{4+49} = \sqrt{53}
     $$
   - The unit vector is:
     $$
     \left\langle \frac{2}{\sqrt{53}}, \frac{7}{\sqrt{53}} \right\rangle
     $$

2. For the unit vector in the opposite direction of $$ \langle 9,2,2\rangle $$:

- Compute the magnitude:
     $$
     \|\langle 9,2,2\rangle\| = \sqrt{9^2 + 2^2 + 2^2} = \sqrt{81+4+4} = \sqrt{89}
     $$
   - The unit vector in the opposite direction is:
     $$
     \left\langle -\frac{9}{\sqrt{89}}, -\frac{2}{\sqrt{89}}, -\frac{2}{\sqrt{89}} \right\rangle
     $$

3. For the unit vector in the same direction as the vector from $$ P=(10,4) $$ to $$ Q=(2,3) $$:

- Find the direction vector from $$ P $$ to $$ Q $$:
     $$
     Q - P = \langle 2-10,\, 3-4 \rangle = \langle -8, -1 \rangle
     $$
   - Compute its magnitude:
     $$
     \sqrt{(-8)^2 + (-1)^2} = \sqrt{64+1} = \sqrt{65}
     $$
   - The unit vector is:
     $$
     \left\langle -\frac{8}{\sqrt{65}}, -\frac{1}{\sqrt{65}} \right\rangle
     $$
1. The unit vector in the same direction as $$ \langle 2,7\rangle $$ is $$ \left\langle \frac{2}{\sqrt{53}}, \frac{7}{\sqrt{53}} \right\rangle $$. 2. The unit vector in the opposite direction of $$ \langle 9,2,2\rangle $$ is $$ \left\langle -\frac{9}{\sqrt{89}}, -\frac{2}{\sqrt{89}}, -\frac{2}{\sqrt{89}} \right\rangle $$. 3. The unit vector in the same direction as the vector from $$ P=(10,4) $$ to $$ Q=(2,3) $$ is $$ \left\langle -\frac{8}{\sqrt{65}}, -\frac{1}{\sqrt{65}} \right\rangle $$.

Find unit vectors that satisfy the given conditions below.
The unit vector in the same direction as .
The unit vector in the opposite direction of .
The unit vector that has the same direction as the vector from the point to the point
.
Question Help: Video 1 Video 2
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Find unit vectors that satisfy the given conditions below. The unit vector in the same direction as . The unit vector in the opposite direction of . The unit vector that has the same direction as the vector from the point to the point . Question Help: Video 1 Video 2 Submit Question

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Latest Pre Calculus Questions

Find unit vectors that satisfy the given conditions below.
The unit vector in the same direction as .
The unit vector in the opposite direction of .
The unit vector that has the same direction as the vector from the point to the point
.
Question Help: Video 1 Video 2
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