10. Four points that are coplanar 11. Three lines that intersect at one point 12. A line and a plane that intersect at one point

Q: 4. A quadrilateral has vertices (4, 1), (1, 7), (- 6, 0) and (-1,-9). Show that the mid-points of…

A: As per the guidelines I am answering only first question. Kindly reupload and ask to answer other…

Q: 5. Prove analytically that a quadrilateral with diagonals that bisect each other is a parallelogram.…

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Q: . A pizza restaurant will deliver up to 5 miles. The restaurant is located at the origin on a…

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Q: 4. Determine which values of t E R result in span ((0, 1, -1), (1, 2, 1), (t, -1, 4)) being (i) a…

A: {(0, 1, -1), (1, 2, 1)} is a linearly independent set. (When there are only two vectors, it's…

Q: 11. Consider the plane and the line with these equations: 0 = 2x + y -z + 10 a) :. e must b) Find…

A: The line passes through (-4, 2, e) and has direction ratios  3, f, 1 In case (a) the line lies on…

Q: 26. Which of the following planes are identical, which are parallel to each other, and which are…

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Q: The line whose equation is given as: (x-2z-2=0, y-22 -0) intersects the plane (x-2y+2-1-0) at the…

A: Given: x-2z-2=0 y-2z=0 equation of plane x-2y+z-1=0

Q: 9. Prove, by coordinate geometry that QRST is a parallelogram. Q(0

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Q: 4. Points P(1, 2, 0), Q(2, 3, -1) and R(-1, 1, 5) lie on a plane. Find the Cartesian equation of the…

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Q: 5. Find the point of intersection of the given plane and line. Plane: 2x - y+3z=7 Line: x=-1+t y…

A: We have to find  point of intersection .

Q: 4. If two lines do not intersect, can a third line be drawn perpendicular to them?

A: This is a problem related to intersection of the line. Based on the general formula and concepts we…

Q: 8. Let P(1,2,3), Q(1,-1,-2), and R(0,0,0) be the three points in R³ a. Find an equation of the plane…

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

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Q: Exercise 1.5. Consider coordinates in the plane; i.e., pairs (a, b) where a,b e R. Recall that two…

A: Given: a,b To find: Program

Q: Consider two lines. Line L1 is defined by 1, and Line L2 is defined by y = 3x y = 2x + 4. A. Without…

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Q: 3. Write an equation of the plane that is determined by the lines given by == and ==국 -2 z-2 -3 4 -1

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Q: 8. What is the necessary condition for two lines to be parallel?

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Q: 36. Given two points A(-2,4) and B(x,-8), what must be the value of x so that a line passing through…

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Q: 9. A committee of senior and junior executives will be formed to decide on recruitment issues. If…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Let points A, B, C, and D be as follows: A=(3, 1, 2), B=(-1,3,5), C= (0, 2, 2), D =(4, 5, 1) a)…

A: The distance of a plane is defined as the algebraic expression that gives the pairs of points in the…

Q: ind the line of intersection of the planes x+y+z=1 and y+z=0

A: The given planes are x+y+z=1 and y+z=0. It is required to find the equation of line of intersection.…

Q: 8. There are 5 points on a plane, no three of which are collinear. How many different lines can be…

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