Question

Find the vector and parametric equations for the line through the point P=(5,−2,3) and the point Q=(2,−7,8).

Vectors and spaces
ANSWERED
asked 2020-10-18
Find the vector and parametric equations for the line through the point P=(5,−2,3) and the point Q=(2,−7,8).

Answers (1)

2020-10-19

Here think about your starting point, say it is P.
Start at (5,−2,3)(5,−2,3) then to get to Q, you must travel in the direction of Q which is given by Q−P=(2,−7,8)−(5,−2,3)=(−3,−5,5). Now, traveling this direction in any scaled value gives you a line determined by the following vector equation:
(5,−2,3)+t(−3,−5,5)
which you can write in parametric form:
x=5−3t, y=−2−3t, and z=3+5t
notice that all we did was just write it in a form that represents a formula for each point (x,y,z)(x,y,z).

0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-05-07
Find a vector equation and parametric equations for the line segment that joins P to Q.
P(1, -1, 5), Q(5, 6, 1)
vector equation r(t) = ?
parametric equations (x(t), y(t), z(t)) = ?
asked 2021-05-14
Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7)
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R
b) Find the area of the triangle PQR
asked 2021-05-29
Find a vector equation and parametric equations for the line segment that joins P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)
asked 2021-05-03
Find a nonzero vector orthogonal to the plane through the points P, Q, and R, P(0,-2,0), Q(4,1,-2), R(5,3,1)
asked 2021-06-01
Find the vectors T, N, and B at the given point.
\(r(t) =\) and point \(<4,-\frac{16}{3},-2>\)
asked 2021-06-12
Find the principal unit normal vector to the curve at the specified value of the parameter
\(r(t)=ti+\frac{6}{t}j , t=3\)
asked 2021-05-01
The average height of a 2 year old boy is 38 inches; an 8 year old averages 56 inches. Use this information to write a linear equation that models the height (in inches), y, in terms of the age (in years), x. Use the linear equation to predict the average height of a 5 year-old boy.
asked 2021-03-29
Find parametric equations for the curve with the given properties.
The line with slope -2, passing through (-10,-20)
asked 2021-04-14
Find parametric equations for the curve with the given properties.
The line with slope \(\displaystyle{\frac{{{1}}}{{{2}}}}\), passing through (4,-1)
asked 2021-01-30

A line L through the origin in \(\displaystyle\mathbb{R}^{{3}}\) can be represented by parametric equations of the form x = at, y = bt, and z = ct. Use these equations to show that L is a subspase of \(RR^3\)  by showing that if \(v_1=(x_1,y_1,z_1)\ and\ v_2=(x_2,y_2,z_2)\)  are points on L and k is any real number, then \(kv_1\ and\ v_1+v_2\)  are also points on L.

You might be interested in

...