20. Determine the angle between a = (5, 3, 0) and b = (-1, 0, 8) 21. The vertices of a quadrilateral are A = [0,3,5], B = [-3,-1,17], C = [4,-3,15] & D = [7,1,3]. Prove that ABCD is a parallelogram. x-1 y-2 z+1 22. Determine the value of k for which the direction vectors of the lines || = and k 2 k-1 x+3 Ꮓ y = -1 are perpendicular. -2 1

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: coordinates of D. А. D(-5, 4) В. D(8, 2) С. D(14, 4) D. D(4, 1)

A: Use property of parallelogram to solve

Q: _8. What type of quadrilateral is PQRS? Given: P(-5, 2); Q(4,5); R(6, -1); S(-3,4) b. rectangle _9.…

A: Solve above questions.

Q: 11. The vertices of a triangle are P(-6, –3), Q-3, –6), and R(-5, –2). Name the vertices of the…

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Q: Do the points (0.5, 1), (1, 1.2), (2, 2) lie on a line?

A: Three points will lie on same line if slope of any two point is same as other two points, taken two…

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

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Q: the coordinates of the image. 8. Square PQRS with vertices P(-5, 4), Q(2,8), R(6, 1), and S(-1, -3):…

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Q: 7. Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(10,…

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Q: Consider the points A(-10,8), B(-1,-13), C(-4,-15). Given that ABCD is a parallelogram, find the…

A:

Q: Prove that the points represent the vertices of a parallelogram. You may use the method of your…

A: The given points are A-4,7, B3,0, C2,-5 and D-5,2. Note that, the distance between 2 points x1,y1…

Q: 1)calculate dedy ry where D is a parallelogram with vertices (0,0).(5,-1).(3,1) and (8,0) tip:Use…

A: Here we will use change of variable to find integral If we want to integrate f(x,y) over the region…

Q: 9. A rhombus is drawn in the standard xy-coordinate plane. The line 2x+y= 4 includes one of the…

A:

Q: 2) The vertices of quadrilateral RYAN are R(2-2), Y(4,5), A(-6,4), and N(-8,–2). Use coordinate…

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Q: 33. Sketch the diagram that you would use to find the magnitude of the sum of a and b if the angle…

A: 20. To find the angle between two vectors \(\vec{a}\) and \(\vec{b}\), you can use the formula…

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: 6. A line segment has endpoints at 4(-1, -8) and B(5, -4). Which of the following are the…

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Q: 27. Let ABC be a triangle with vertices A = (-3,0), B = (0, 6), C = (3, 0). Let P be a point on the…

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Q: For A(-1,2); B(6,4); C (1, – 20), how many different points D could be chosen if ABCD is a…

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Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: 38. A rectangle with sides parallel to the axes has vertices at (3, - 2) and (-4, – 7). a) Find the…

A: Explanation of the answer is as follows

Q: 2- The line perpendicular to the triangular (PQR) and through the point (P) if P(1,-1,2), Q(0,3,1),…

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Q: 8. Which coordinate grid shows a point 3 represented by (;, -3)? (6.18, 6.1E, 6.1F)

A: The given coordinate is ( -3/2 , -3) x coordinate is  -3/2  y coordinate is  -3 It means that the…

Q: Give the coordinates of C" of Rhombus ABCD with vertices A(1,-8), B(3,-9). C(4.-11), D(2.-10) after…

A: Given, vertices A(1,-8), B(3,-9), C(4,-1), D(2,-10) after reflecting across the x-axis sign of y…