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Edmund Conti

Answered question

2021-12-04

Represent the line segment from Pto Qby a vector-valued function. (Pcorresponds to t= 0. Q corresponds to t=1.)

P (- 7, - 3, - 1), Q (- 2, - 9, - 9)

Answer & Explanation

Marlene Broomfield

Beginner2021-12-05Added 15 answers

Step1
We have to representa line segment in the vector-valued function that starts from a point P and end at Q as it is given that P corresponds to t= 0 and Q corresponds to t= 1
the points given to us is

P = (- 7, - 3, - 1) and Q = (- 2, - 9, - 9)

the general form of the line represented by vector-valued function is

r (t) = r_{0} + t v

(1)
where

r_{0}

is the initial position
v isthe position vector
t is the time
Step2
to calculate v we use the formula as

(x_{1}, y_{1}, z_{1}) = (- 7, - 3, - 1) and (x_{2}, y_{2}, z_{2}) = (- 2, - 9, - 9)

and

\vec{v} = (x_{2} - x_{1}, y_{2} - y_{1}, z_{2} - z_{1})

\vec{v} = (- 2 - (- 7), - 9 - (- 3), - 9 - (- 1))

\vec{v} = (5, - 6, - 8)

and

r_{0} = (x_{1}, y_{1}, z_{1}) = (- 7, - 3, - 1)

Step3
putting the values of 1 and vin equation (1) we get

r (t) = r_{0} + t v

r (t) = (- 7, - 3, - 1) + t (5, - 6, - 8)

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