Think of it in terms of adding vectors - one vector from the origin to a given point on the line, and another vector from the given point on the line to an arbitrary point on the line.somebodyelse5 said:Homework Statement
Find the vector and parametric equations for the line through the point P(-3, 3, -5) and the point Q(-7, 4, -1).
Homework Equations
N/A
The Attempt at a Solution
r= <__,__,-5>+t<__,__,4> The -5 and 4 are given.
Heres what I have so far. r=<-3,3-5>+t<__,__,__>
I am totally lost on how to find those other two points and the equations.
Mark44 said:Think of it in terms of adding vectors - one vector from the origin to a given point on the line, and another vector from the given point on the line to an arbitrary point on the line.
Your vector equation of the line will be r = OP + t*PQ
What you're missing is a vector that gives the direction of the line.
Mark44 said:How do you find the vector from P to Q? You don't multiply - that makes no sense at all.
A line is a one-dimensional geometric figure that extends infinitely in both directions. In calculus 2, it is often represented by an equation in the form of y=mx+b, where m is the slope and b is the y-intercept. A plane, on the other hand, is a two-dimensional figure that extends infinitely in all directions. In calculus 2, it is represented by an equation in the form of Ax + By + Cz = D, where A, B, and C are the coefficients and D is the constant term.
To find the equation of a line in calculus 2, you need to know the slope and a point on the line. You can use the point-slope form of a line, y-y1 = m(x-x1), where (x1,y1) is the given point and m is the slope. Alternatively, you can use the two-point form of a line, (y-y1)/(x-x1) = (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two given points on the line.
The normal vector of a plane in calculus 2 is a vector that is perpendicular to the plane. It is represented by the coefficients of the plane equation, (A,B,C). The normal vector is important in determining the orientation and angles of the plane in relation to other geometric figures.
To find the intersection of a line and a plane in calculus 2, you need to solve for the coordinates of the point where they intersect. This can be done by setting the equations of the line and the plane equal to each other and solving for the variables.
A vector equation in calculus 2 is an equation that represents a line or plane using vectors. It is written in the form of r = r0 + tv, where r is the position vector, r0 is a known point on the line or plane, t is a scalar, and v is the direction vector. This form is useful for calculating distances, angles, and projections in 3-dimensional space.