Demonstrate how a central projection can transform parallel lines into intersectin lines.

Q: There are 8 points in a Plane out of which 5 are collinear how many straight lines can be formed?

A: We have given that  There are 8 points in a Plane out of which 5 are collinear how many straight…

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it.

A:

Q: What are the Secant Lines?

A: If we join any two points on a given curve then the joining line is called the Secant Line. Secant…

Q: Verify that the two planes are parallel.

A: -x+6y+3z = 6-13x +2y+z = 7∵-1-13=62=31=3then the planes are parallel

Q: Write down the equation of any plane through the origin.

A: Write down the equation of any plane through the origin.

Q: Can two horizontal planes intersect?

A: Explanation: If two planes are horizontal, it means both are parallel to the x-axis.

Q: Consider the point (3,4,5) What is the projection of the point on the xy-plane?

A: The given point is (3,4,5).

Q: Postulate 12 states that if two points lie in a plane, the line that contains them lies in the…

A: We need to determine whether the given statement is true or false. Postulate 12 states that if two…

Q: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

Q: Use Clairaut's theorem to draw the geodesics of the catenoid

A: Solution :-

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: If the straight lines are coplaner then they are?

A:

Q: find the distance in space between the points (5,3,-2) and (0,0,1)

A: Use distance formula between two points

Q: What are the projections of the point (−2, 3, 4) on the xy-, xz-, and yz-planes? Draw a picture and…

A: Given, the point (-2, 3, 4), we have to find the projections of this point on the xy-, yz-, and…

Q: A __________ is the set of all points in a plane that are equidistant from a fixed line (called the…

A:

Q: Exercise 2. Find a formula for the curve which is traced by the motion of a fixed point on a wheel…

A:

Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

A:

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

A:

Q: Find the plane determined by the intersecting lines.

A:

Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: Write the characterisation of two parallel lines in terms of the cross product and prove it

A:

Q: By vector methods, show that the line segment joining the midpoints of two sides of a triangle is…

A: To prove :- The line segment joining the midpoints of two sides of a triangle is parallel to the…

Q: What is the locus of points in space equidistant from two parallel planes?

A: Locus: If the two lines are in Rn the points equidistant from them form an n−1 dimensional…

Q: Write the characterisation of two parallel planes (given in general forms) in terms of the cross…

A:

Q: Explain how to find the distance between two parallel planes.

A: Explain how to find the distance between two parallel planes.

Q: What does the cross product of two planes that intersect at a line represent in terms of the line of…

A: Firstly, let us understand what a normal vector is. Normal Vector of a plane is a vector which is…

Q: A simple contour that is not closed can cross itself

A: Contour means simply a curve and simple means curve that doesn't intersect itself. If a simple…

Q: What are the projections of the point (6, –3, 5) on the coordinate planes? On the xy-plane: ( On the…

A:

Q: What is plane and cartesian plane?

A:

Q: Use a directed line segment to represent the vector.u = (2, −4)

A:

Q: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to…

A:

Q: Explain why a line in hyperbolic geometry must contain two distinct ideal points.

A: We have to answer given Questions.

Q: Prove that parallel lines determine only one plane.

A:

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: Prove that the line joining the midpoint of a median to a vertex of the triangle trisects the side…

A: Here ask to prove the line joining the midpoint of a median to a vertex of the triangle trisectsthe…

Q: What are the coordinates of the point on the directed line segment from (- to (10,-2) that…

A: the given points are: (-4,-10), (10,-2)If (x,y) be the coordinate of the point than partition the…

Q: Calculate the distance between the points M-(-2,-2) and H-(3,-8) in the coordinate plane. Give an…

A: To find the distance between the points M=(-2,-2) & H=(3,-8). Now, note that the distance…

Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: 5, what is the speed of the plane?

A:

Q: Construct the perpendicular bisector.

A: 1)

Q: What are the coordinates of the point on the directed line segment from (–10, –1) to (10,-6) that…

A: If a point on the directed line segment from (x1, y1) to (x2, y2) partitions the segment into a…

Q: Prove that the midpoints of a parallelogram bisect each other using coordinate geometry.

A:

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Do two intersecting lines determine a plane?

A: Two lines intersect at only one point.

Q: Does a plane have edges?

A: A plane is infinite by the notion. So it does not have an edge.

Q: how do i prove that the diagonals of a parallelogram bisect each other ? Then have to name…

A:

Q: Show that triangle with vertices p(6,-7),q(11,-3) and r(2,-2) is a right angle triangle using…

A:

Q: Do two distinct lines in space determine a unique plane? Explain.

A: Yes ,  two distinct lines in space determine a unique plane

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.