44. Use the cross product to find the area of the triangle with vertices P = (1, 1, 5), Q = (3, 4, 3), and R = (1, 5, 7) (Figure 20). R FIGURE 20

Q: Find the area of the triangle with the given vertices.(1, 1), (−1, 1), (0, −2)

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Q: 27. Find the area of the parallelogram with vertices A (-3, 0), B (-1, 3), C (5, 2), and D (3, –1).

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Q: Sketch the triangle with vertices O, P = (0,7, 3) and Q = (7,4,0) and compute its area using cross…

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Q: what are the coordinates of the point on the directed line segment from (-6,-1) to (6,-9) that…

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Q: Suppose that you run along three different paths from location A to location B. Along which path (s)…

A: Distance is the total distance travelled between 2 points Displacement is the shortest distance…

Q: 47. Sketch the triangle with vertices at the origin 0, P = (3,3,0), and Q = (0, 3,3), and compute…

A: The triangle OPQ formed by the three points P (3, 3, 0), Q (0, 3, 3) and origin O (0, 0, 0) is shown…

Q: Sketch the triangle with vertices O, P = (0,7,2) and Q = (5,0,4) and compute its area using cross…

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Q: Find the perimeter of the polygon with the vertices Q(−3, 2), R(1, 2),  S(1,−2),Q(−3, 2), R(1, 2),…

A: Perimeter of polygon = Sum of length of all sidesLet A(x1, y1) and B(x2, y2) . Then,   Length of…

Q: Find the area of the parallelogram with vertices  K(2, 1, 1), L(2, 2, 4), M(4, 6, 4), and N(4, 5,…

A: To Determine  The area of the parallelogram with vertices  K(2, 1, 1), L(2, 2, 4), M(4, 6, 4), and…

Q: Find the area of the triangle with vertices P(1,3,–4), Q(0, 0,0) and

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Q: Find the area of the triangle with vertices P=(1,1,0), Q=(0,2,1) and R=(2,0,0).

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Q: Find the point E that partitions the directed segment CD  in a ratio of 1:5, given the points…

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Q: 2. Find the area of the triangle with vertices (0,0), (3,1) and (1,2)

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Q: Find the point Q along the directed line segment from point R(-3,3) to point S(6,-3) that divides…

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Q: What are the coordinates of the point on the directed line segment from (-8,-2) to (6, 2) that…

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Q: Find the distance between the points P(, 6,7) and Q(, 1,, 5)

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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: Find the area of the trianlge with vertices P(1,0,1), Q(-2,1,3) and R(4,2,5). Show your work. 5.

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Q: Find the perimeter of a triangle with vertices S(4, 5), T(-2, -3), and W(5, - 4).

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Q: Find the point R that breaks the directed segment PQ  in a ratio of 1:3, given point P(-4,5)  and…

A: Find the point R which breaks the segment PQ in the ratio 1:3 using section formula

Q: Find the area of the parallelogram with vertices P(3, 3, 2), Q(6, 5, 4), R(11, 9, 13), and S(8, 7,…

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Q: 6- Find the distance from the Point AC,2,1) to the line joining the too Points B Co,5,2), C(3,2,7)

A: fghk

Q: Compute the areas of the polygons in Figure 28. Check your result for the area of the triangle in…

A: Consider the provided information, Find the area of the of the triangle.

Q: Draw the image of quadrilateral ABCD under the translation (z, y)-(-7,y+1).

A: from the diagram coordinate of quadrilateral ABCD   is   A(6,-5)    B(0,-3)     C(5,-2)   and (5,-4)

Q: A trapezoid is shown in the coordinate plane. 10 9- 8 7- 6- 5- 4 3- 2- -10 -9 -8 -7 -6 -5 -4 -3 -2…

A: Given is a trapezoid, when we divide it into 2 parts   equally, the left and right side will be…

Q: Evaluate ry dr + r'dy, where C is the rectangle with vertices (0,0), (3,0), (3,1), and (0,1)

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Q: Find the area of a triangle with the points A(1,0,0), B(0,1,0), C(0,0, 1) as it vertices by using…

A: Question: Find the area of the triangle with the points A1,0,0, B0,1,0, C0,0,1 as its vertices by…

Q: Find the area of the parallelogram with vertices P(2, 3, 3), Q(5, 5, 6), R(10, 9, 14), and S(7, 7,…

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Q: Find the area of the parallelogram that has u = (1, 3, 0) and v = (−1, 0, 2) as adjacent sides.

A: Now cross product is,

Q: Find the area of the triangle with vertices: Q(4,-1,4), R(6,0,6), S(8,-4,7).

A: To find  The area of a traingle with vertices.

Q: Verify that the points A(0, 3, 2), B(1, 5, 5), C(6, 9, 5), D(5, 7, 2) are the vertices of a…

A: Given points are A(0,3,2), B(1,5,5), C(6,9,5), D(5,7,2).

Q: Evaluate O ry*da + x°dy, where C is the rectangle with vertices (0,0), (1,0), (1,5), and (0,5)

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Q: Find the area of the parallelogram spanned by v = (1, 1, 1) and w = (0, 0, 2).

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Q: Verify that the points A(2, −3, 1), B(6, 5, −1), C(7, 2, 2), D(3, −6, 4) are the vertices of a…

A: Given: The points A2,-3,1, B6,5,-1, C7,2,2, D3,-6,4.

Q: What are the coordinates of the point on the directed line segment from (-6,-6) to (9,-1) that…

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Q: Find the midpoint of the segment joining (4, −6) and (2, −6). (x, y) =?

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Q: What are the coordinates of the point on the directed line segment from (-10,-5) to (5,1) that…

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Q: Find the area of the triangle having vertices at P (1,3,2), Q (-2,1,3) and R (3,-2,-1)

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Q: Which of the letters B, O, K, I, V, F, X, D, L, and Y are their own images under a rotation by an…

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Q: A directed segment  QR¯¯¯¯¯QR¯ with endpoints at  Q (2, 1)Q (2, 1) and  R (8, 13)R (8, 13) is…

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Q: Find the area of the triangle with vertices P(1, 6, –2), Q(0,0,0) and R(2,4, 1). - NOTE: Enter the…

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Q: Use the cross product to find the area of the parallelogram whose vertices are (0,0,0) , (0,2,1),…

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Q: Find the area of the parallelogram with vertices at (3, –3), (11, 1), (12,-5), and (20, –1). Area =

A:

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: What are the coordinates of the point on the directed line segment from (-1, –2) to (9, –10) that…

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Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: 10. Triangle JLM with vertices J(-5, 7), L(8, 3), and M(-3, -1): (0, – 5) J'(__ L’(__ M’ (__,

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Q: Find the COM of the laminas in Figure 26 obtained by removing squares of side 2 from a square of…

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Q: Find the  area of the triangle with vertices P(1,3,5) Q(-1,4,-4) and  R(1,5,4)

A: P1,3,5 Q=-1,4,-4  R1,5,4PQ=OQ-OP     =-i∧+4j∧-4k∧-i∧-3j∧-5k∧PQ=-2i∧+j∧-9k∧PR=OR-OP     =i∧…