Question

Vectors: Find the vector from the point A=(−1,−7,3) to the point B=(3,−2,9).

Answer 1

Answer:

$\overrightarrow {AB} = (4,5,6)$

1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F

2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F

3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T

4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F

5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F

Step-by-step explanation:

The vector AB is the vectorial difference between point A and B, that is:

$\overrightarrow {AB} = \vec B - \vec A$

Given that $\vec A = (-1,-7,3)$ and $\vec B = (3,-2,9)$, the vector AB is:

$\overrightarrow {AB} = (3,-2,9)-(-1,-7,3)$

$\overrightarrow{AB} = (3-(-1),-2-(-7),9-3)$

$\overrightarrow {AB} = (4,5,6)$

The vectorial equation of the line is represented by:

$\langle x, y, z\rangle = \vec A + t \cdot \overrightarrow {AB}$

Where $t$ is the parametric variable, dimensionless. Given that $\vec A = (-1,-7,3)$ and $\overrightarrow {AB} = (4,5,6)$

$\langle x,y,z \rangle = \langle -1,-7,3 \rangle + t\cdot \langle 4,5,6 \rangle$

Finally, the list of questions are now checked:

1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉 F

2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉 F

3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉 T

4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉 F

5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉 F