Given the points P = (2,3, 4), Q = (4,–1,5) and R = (-2,5,6) : a. Find a parametric or vector equation of the line through P and Q. F1) = ( b. Find an equation of the plane through the three points.

Q: Consider the points A=(2,7,-4) and B=(4,5,7) in R3, one way to write the parametric equation of the…

A: Given :- Consider the points A = (2, 7, - 4) and B = (4, 5, 7) in R³, To find:- one way to write the…

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

A:

Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: Find the vector, parametric, and symmetric equations of the line which passes through the points A =…

A: Given points are: A=3,1,-1 and B=7,0,1 To find the vector, parametric, and symmetric equations

Q: Write down the position vectors of any two points on the line ˜ r · (3i − 4j) + 2 = 0 and hence find…

A:

Q: Find the symmetrical equation of the line perpendicular to the plane passing through the points…

A: Given problem:- Find the symmetrical equation of the line perpendicular to the plane passing through…

Q: Find the equation of the plane that contains the point (4, – 1, 3) and is perpendicular to the…

A:

Q: Given the points A(2,6,0) and B(3,5,6) determine the equation of a line vector in parametrix form

A:

Q: c-) Represent in a Cartesian system the graph of these two lines. d-) Give a vector equation for…

A:

Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

A:

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A: Given that : P = ( 1, 0 ) and d = -13 .

Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

A:

Q: Suppose a line is given parametrically by the equation L(t) = (-4t, –4 – 3t, 4 + 4t) Then the vector…

A: topic - equation of line

Q: draw the plane given by the equation  x + y + z = 0

A: x+y+z=0 It is a plane passing through origin.

Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

A:

Q: Find the equation of a plane that is perpendicular to the vector i+ 2j+5 k and passing through the…

A:

Q: Find parametric equation of the line joining points P{(2,4, –1) and P2(5,0, 7). Where does it…

A: To do this we need the vector V→ that will be parallel to the line. This can be any vector as long…

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

A:

Q: Find parametric equations for the line through P(8, −7, 9) perpendicular to the vectors A = ⟨3, −1,…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  given vectors are

Q: Which of the following is a direction vector for the plane with Cartesian equation 3x -2y - 5z + 3 =…

A: To find a direction vector for the given plane. The general form of plane with cartesian equation…

Q: Find the parametric equation of the line that passes through the point P(2,4, –2) and is parallel to…

A: Parametric equation of line that passes through the point P(x0, y0, z0)& parallel to vector a =…

Q: Suppose a line is given parametrically by the equation L(t) = (4+ 3t, -4 – 5t, 2 – 2t) %3D Then the…

A: Compare with general equation of line in parametric form

Q: c) Is the point (4,3, 3) on the line (L1) ? Why or why not ? d) Determine the vector equation of the…

A:

Q: The vector from the origin to point A is given as 6a, – 2a, – 4a., and the unit vector directed from…

A: The vector from the origin to point A is 6ax-2ay-4az Therefore, vector A is A→=6,-2,-4 Now, the unit…

Q: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

Q: Given the points P = (2,3,4), Q = (4,–1,5) and R = (-2,5,6) : a. Find a parametric or vector…

A:

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A:

Q: 27. Are the points P(1, 2), e(7,3), and R(-2, 1) on the line with vector equation = (19,5) + s(6,1),…

A: According to our terms and conditions I have solved first question for next question repost

Q: a) Find the vector that is parallel to the tanget to the circle x2 + y2 = 100 at the point (3,-4).…

A: a) Given equation of circle, x2 + y2 = 100. We have to find the vector equation which is parallel to…

Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

A:

Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  . the given direction…

Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

A: The equation of the line is: x = 2 + 4t y = 5 - 8t z = 9t From the given equation of the line we…

Q: Write the line through p = (3, 2, 2) in the direction of v = (-1, –4, 2) in vector parametric form:…

A: We have to write the line trough p=3,2,2 in the direction of v¯=-1,-4,2 in vector parametric form.

Q: Find the vector form of the equation of the line inR3 that passes through P = ( - 1, 0, 3) and is…

A: Find the vector form of equation of line passing through point  P=-1,0,3 and perpendicular to the…

Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

A:

Q: The plane that contains the point (3, –1, –4) and the line with equation = y – 1 = 3z is orthogonal…

A: Let:x-02=y-11=z-013=kL: x=2k, y=k+1,  z=k3P1:(3, -1, -4)Put k=0, k=1P2: (0, 1, 0)P3: (2, 2,…

Q: -1. Through (1,5, 2) perpendicular to 37 – J + 4k .

A:

Q: Use the component form to generate an equation for the plane through P1(4, 1, 5) normal to n1 = i -…

A: Concept - If a plane is passing through (x0, y0, z0) and normal vector is A, B, C.Then equation of…

Q: he intercepts of the plane given by

A: Intercepts of the plane are (3,5,3).

Q: a) The line y =- 5x + 9, in VECTOR form (R?).

A:

Q: Find the equation of the plane containing the following two lines: L1 : te R 1 L2 : +s. seR 1

A:

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A:

Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

Q: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

A:

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…