ху ds (a) C: line segment from (0, 0) to (5, 4) (b) C: counterclockwise around the triangle with vertices (0, 0), (4, 0), and (0, 2)

Q: 3,0 on a coordinate plane

A: we have to plot (3,0) on a coordinate plane using graph we can plot (3,0) on coordinate plane as…

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

A:

Q: Find the distance from the point (-5, -1, -3) to the plane 5x + 3y + 2z = 1

A:

Q: 11. Determine whether the lines are parallel, perpendicular, or neither. Show your work. 4 Line 1:…

A: Since the product of slopes is -1 hence these lines are perpendicular.

Q: The plane passes through the point (18, -16, 9) and contains the line given by = = z . 1.

A:

Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

A:

Q: 2)Passes point (1,3,7) and orthogonal to xy- plane.

A: The line which is orthogonal to x-y plane is lies on z-axis. Therefore the direction ratio's of the…

Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

A:

Q: What is the image of the point (2,-3) after the transformationr y-axis 1) (2,3) 2) (-2,-3) 3) (-2,3)…

A:

Q: Use calculus of variation to derive the shortest line (equation) that joining points (x,y,z) =…

A: Given plane -   7x + 2y + 3z = 7 Parametric equation will be =  (1 - t, 0- 2t, 0 - t) Hence,

Q: 9 What is the distance between points (-10, 6) and (-2, 2) on a coordinate plane?

A:

Q: 2) through: (-1, 5), parallel to y=-9x – 5 4) through: (-3, 4), parallel to y=-- 4 +3 3

A:

Q: Find the distance from the point (-1, 3, -1) to the plane -1x + 2y -5z=1.

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: 11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

A: This question is related to coordinate geometry, We will solve it using given information.

Q: Find the equation of the line through point (3,7,-11) y is perpendicular to the xz-plane

A:

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2) , the robot turns 90°…

A: The robot begins moving at (2,1) and reaches at (5, 2) taking a linear path. So, the equation of a…

Q: 17. A robot begins moving on a linear path at (3, 1). When it reaches (5,2), the robot turns 90°…

A: Here, given that the robot is moving on a linear path from (3,1) to (5,2). Therefore, the slope of…

Q: 3- Find an equation of the Plane perpendicular to the line through (2,2,-9) and (7,-1,3) and…

A: To Find: Equation of plane perpendicular to the line through the points (2,2,-9) and (7,-1,3) and…

Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

A:

Q: (a) The curve with equation 2 y 3 + y2 - y 5   = x 4 -2x3  +x 2  has been likened to a bouncing…

A:

Q: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

Q: Where does the line through (1,0,1) and (4,-2,2) intersect the plane x+y+z=6?

A:

Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

A:

Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: Linear equation

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2), the robot turns 90°…

A: We have to find the y-coordinate.

Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: This is a problem related to linear coordinates. based on the diagram shown in solution we will…

Q: Find an equation of the plane through (-8, –4, –5) that is 2 = t, y + 3 | perpendicular to the line…

A:

Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

A:

Q: 6. parallel to y%3D through (-3, 6)

A:

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A:

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y - z = -2? (x, y, z)…

A:

Q: 3. Through the point (4, -5, 20) and perpendicular to the plane x + 3y – 6z - 8 = 0.

A:

Q: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A:

Q: CISES parallelogram. 2. 0.3!

A: Given query is to find the area of the parallelogram.

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

A:

Q: Find the distance from the point (5, -4, 1) to the plane −3x−2y−3z=−4

A:

Q: Find the distance from the point (-2, 2, 3) to the plane -3x + y – z = 9.

A:

Q: 4. In general, if the line y is rotated 90° about (0, 0), explain how you can find the equation of…

A:

Q: Find the distance from the point (3, 1,0) to the line given by symmetric equations *** =-3, y= 1.

A: Given that: The point is: (3, -1, 0) and equation of line is:         x+42=z-3, y=1

Q: Find the distance from the point (-2, 1, 4) to the plane x = 3

A: Given: The point -2,1,4 and plane x=3 To find: Distance from the given point to the given plane.

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: 6. Find the distance between the point (-3, 1) and the line 4x + 3y + 4 = 0.

A:

Q: Find the distance between points A(1,1,0) and B(1,0,1)?

A: A1, 1, 0 & B1, 0, 1.

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

A:

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

A:

Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.