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〉

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:

Given that and , the vector AB is:

The vectorial equation of the line is represented by:

Where is the parametric variable, dimensionless. Given that and

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

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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