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

Equations of lines: Consider the vector equation of the line through the two points listed above. For each equation listed below, answer T if the equation represents the line, and F if it does not.

Here is the list of questions:

1. 〈x,y,z〉=〈−1,−7,3〉+t〈−4,−5,−6〉

2. 〈x,y,z〉=〈−1,−7,3〉+t〈3,−2,9〉

3. 〈x,y,z〉=〈−1,−7,3〉+t〈4,5,6〉

4. 〈x,y,z〉=〈3,−2,9〉+t〈−1,−7,3〉

5. 〈x,y,z〉=〈3,−2,9〉+t〈4,5,6〉

Respuesta :

xero099

Answer:

[tex]\overrightarrow {AB} = (4,5,6)[/tex]

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:

[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]

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

[tex]\overrightarrow {AB} = (3,-2,9)-(-1,-7,3)[/tex]

[tex]\overrightarrow{AB} = (3-(-1),-2-(-7),9-3)[/tex]

[tex]\overrightarrow {AB} = (4,5,6)[/tex]

The vectorial equation of the line is represented by:

[tex]\langle x, y, z\rangle = \vec A + t \cdot \overrightarrow {AB}[/tex]

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

[tex]\langle x,y,z \rangle = \langle -1,-7,3 \rangle + t\cdot \langle 4,5,6 \rangle[/tex]

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

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