Find the equation of the line that goes through the point (1,3, 2) and is parallel to the line (3t – 2, 2t +1, t+4). Given both the vector equation and the parametric equation.

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 an equation of the plane that passes through the given point and is perpendicular to the given…

A: To Find an equation of the plane that passes through the given point (1, 3, -7). First, convert the…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Which of the following is the vector equation of the line through the point (1,2,3) and parallel to…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given that point 2,6,-8   and vector or line ,n=jTo  find : equation of plane Solution :Direction of…

Q: Give the equation of the line in vector form, parametric form and symmetric form. The line through…

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 an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: point = (3,5,-7)n=0 i +1 j + 0 kCartesian equation of plane is Ax+By+Cz+D=0(A,B,C)=( 0,1,0)(x,y,z) =…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Given the points P = (1, 5, –2), Q = (2, 3, –1) and R = (–4, 2, 5). 1. Find the vector that is…

A: Given points, P=1, 5, -2Q=2, 3, -1R=-4, 2, 5 The vectors are…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Express the equations of the lines r · (i −j) + 7 = 0,r · (i + 3j) − 5 = 0 in parametric forms and…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: We have to find the equation of plane.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Question is solved.

Q: Q#2: a) Find the vector, parametric and symmetric equations for the line through the point (5,2,4)…

A: Solution is given below:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Topic = Geometry

Q: Find parametric equations for the line through the points P(-1,- 1, -4) and Q(-4,-7,7). O A. x-t-3 y…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

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: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: 22. Given the symmetric equations t = - and t = +', find the vector equation of the line.

A:

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: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find a parametric equation of the line M throughp and q for the given values of p and q. [Hint: M is…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find the equation of the plane passes through the point P(4,2,1) and perpendicular to the vector…

A: Equation of the plane passing through point P(x0,y0,z0) on the plane and perpendicular to the vector…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find the equation of the line that goes through the point A = (5, –3, –4) and is parallel to the…

A: Given that the line passes through the point A=5,-3,-4 and is parallel to the vector  v=-2,4,3 The…

Q: Find the equation of the line that passes through the point ( 8, 8, 2) and parallel to the vector .…

A: The vector equation of the line which is passing through the point (h, k, l) and parallel to the…

Q: If a line is parallel to the vector 8i + 5j+3k and passes through the point P = (6,2, 4), then the…

A: The line which is parallel to the vector  ai + bj + ck and passes through (x1 , y1 , z1) has the…

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: If a line is parallel to the vector 7i +9j + 9k and passes through the point P = (10,4, 1), then the…

A:

Q: Find the equation of the perpendicular bisector of the line join- ing the points with position…

A: From the given information we can draw this figure

Q: Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is…

A:

Q: Rewrite the vector equation r(t) = (2+t)i + (1+3t)j + (-1+5t)k as the corresponding parametric…

A: We have to find the equation

Q: A:-Find parametric equations for the lines, the line through (4, 7, 1) perpendicular to the vectors…

A: I am attaching image so that you understand each and every step.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find the vector form of the equation of the line in R2 that passes through P= (2, - 1) and is…

A: If a line is parallel to another line, then they have same slope.

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

A: Equation of a plane perpendicular to a, b, c and passing through x0, y0, z0 is, ax-x0+by-y0+cz-z0=0

Q: Given the equation of a sphere a2 + y? + z2 – 4x + 2y + 2z = -5 Which of the following is the vector…

A: Explanation of the answer is as follows

Q: Find the vector equation of the line passing through the point (1, 2, - 4) and x-8 y+19 z-10 x-15 у…

A: To find the equation of line perpendicular to the given lines first we find vector perpendicular to…

Q: If a line is parallel to the vector 7i + 9j+ 9k and passes through the point P= (2,9, 7), then the…

A: Given query is to find the equation of the line.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.