Draw a set of x-, y-, and z-axes and plot the following points: с. С(0, 0, —3) d. D(2, 3, 0) a. A(1, 0, 0) е. Е(2. 0, 3) b. В(0, — 2, 0) f. F(0, 2, 3)

Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Give a geometric description of the set of points whose coordinates satisfy the given conditions. 8)…

A:

Q: Find the point on the line x /a + y/ b = 1 that is closest to the origin.

A:

Q: Plot the points A = ( - 1, 8) and M = (2, 3) in the xy-plane. If M is the midpoint of a line segment…

A: We have the following information    We have to plot the points A = ( - 1, 8) and M = (2, 3) in…

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: Find equation of the plane that contains the lines L1:x = 3 + 5t, y = 6+ 2t, z = 6 + 3t and L2: x =…

A: Equation of plane which passes through L1 is ax-3+by-6+cz-6=0 where 5a+2b+3c=0.

Q: What is the y-coordinate of any point in the xz-plane?

A:

Q: Find an equation of the plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y =…

A:

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

A:

Q: 1 2x 3y + z = 0 and 2 +t - 1 1

A:

Q: parallel

A:

Q: Find the distance of the point (3, 2, –4) from the line r(t) = (1+ 3t, –1+ 2t, 3 – 3t).

A: for finding distance of the point3,2,-4 from line rt=1+3t, -1+2t, 3-3t we assume a point1+3t, -1+2t,…

Q: Draw the line y = 2.x + 1 and its image under reflection in the y-axis.

A: The given line is  y=2x+1 The slope of the line is 2, Y-intercept is 1,0 and X-intercept is -0.5,0.…

Q: . Plot each pair of points and compute the distance between them:(a) (1, 4) and (3, 2) (b) (2, 1)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find equation of the plane that contains the lines L,:x 3+5t, y = 6+2t, z = 7t and L2: x = 7t, y =…

A:

Q: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

A:

Q: find the distance between each pair of points  V(-2,5), M(0,-4)

A: To find the distance between two given points  V(-2, 5) and M(0, - 4)

Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

A: Given points are: 4,-1 and -2,3 The distance between the points 4,-1 and x,y is: d1=x-42+y+12 The…

Q: Find an equation of the plane through the point (2,0, 1) and perpendicular to the line x = 3t, y = 2…

A: To find the equation of a plane passing through (2,0,1) and perpendicular to the line x=3t , y=2-t ,…

Q: ) Find the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, z = 2+ t.

A:

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

A:

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Given that the point (5, 0) a) symmetric with respect to the x axis Substitute the coordinate -y for…

Q: Consider the line which passes through the point P(2 -3, -4), and which is parallel to the line x =…

A:

Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

A:

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: Find the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, Z = 2 + t.

A:

Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

A:

Q: Find the distance between the two straight lines and x=1+1, y=2, z= −1+2+ x=2-t, y=3t4t, z=2t at the…

A:

Q: Find the value of x for which line a is parallel to line b.

A: It is given that,  line a and b are parallel lines,

Q: Find the value of y such that the points are collinear. (1, -2), (-5, y), (-2, –5) y = %D

A:

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: Find a relationship between x and y such that (x, y) is equidistant (the same distance) from the two…

A: If the distance from (x,y) to the points (3,2) & (5,-1) are equal, then the squared distance is…

Q: For the line €: (x, y, z) = (5, - 3, 2) + n(1, 2, - 2), find a) a point of the line. b) a direction…

A: Given parametric equation of line - x, y, z = 5,-3, 2+n1, 2,-2x, y, z = 5,-3, 2+1n, 2n,-2nx, y, z =…

Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

A:

Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

A:

Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

A:

Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: Find the x- and y-coordinates of the labeled point. Ay 10- The coordinates of A are 8- (Type an…

A: The labeled point lies on the x- axis . So its y-coordinates is zero .

Q: Find the distance from the point P(-1,3,-5) to the plane through the three points Q(3, 1, -3). R(4,…

A: The points passing through the plane are: Q3, 1, -3R4, 6, -5S5, -4, -6

Q: Show that the following sets of points are collinear and find the equation of line…

A: Three or more points are collinear, if slope of any two pairs of points is same. With three points…

Q: Find the z-coordinate of the foot of the perpendicular from A(1, 1, 1) on the line joining B(1, 4,…

A: We will solve the problem.

Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

A:

Q: Draw a set of x-, y-, and z-axes and plot the following points: с. С(0, 0, —3) d. D(2, 3, 0) e. Е(2.…

A: Solve by making graph

Q: Find the equations of the line through (2,0, –4) and parallel to each of the planes x + y – z = 0…

A: