80. A median of a tetrahedron is a segment joining a vertex to the cen- troid of the opposite face. The tetrahedron in Figure 22(B) has vertices at the origin and at the terminal points of vectors u, v, and w. Show that the medians intersect at the terminal point of (u + v+ w). A' C P B' u W u W (A) (В)

Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

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Q: Q5/ Find the volume of the Tetrahedron that is determined by three edge vectors â = [1, 0.-3), 5=…

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Q: ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA  respectively and are…

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Q: Vectors are drawn from the center of a regular n-sided polygon in the plane to the vertices of the…

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Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: This question is based on finding the adjacent edges of tetrahedron and dot and cross product use.

Q: 18!- Use the vectors to find the area of the triangle with vertex A(1,0,1), B(0,2,3) and C(2,1,0).

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

Q: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: 5. Two planes are perpendicular if their nommals: a) have a cross product of zero c) have a dot…

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Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

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Q: 1. Find the area of the triangle in the R2 plane whose vertices are given by (0,0), (–1,4) and (7,…

A: 1. The Area of triangle with vertices (x1,y1),(x2,y2),(X3,y3) is given by formula : ∆…

Q: Vectors are drawn from the center of a regular n-sided polygon in the plane to the vertices of the…

A: Let us consider an incomplete regular polygon of n sides and the same polygon after rotation. We…

Q: 6 2 Show that it is vectors are lineas dependent line or independent.

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Q: answer all for an upvote

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

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Q: A triangle has vertices A(1,3), B(7,0) and C(4,6). Determine the equation of Euler's line? Hint:…

A: Sketch the triangle:

Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

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Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: 9. Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R…

A: Since there is multiple questions, we will solve the first question. Repost the question again and…

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

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Q: 4-) Find the a Cute augle between the liue joning the two Points ACY2,3),B(5,1,7) , and the Plane…

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Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

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Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: Three edges of a right triangular prism are defined by the vectors à= [1, 3, 2], b=[2, 2, 4), and =…

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Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

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Q: 1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

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Q: 3) Find the plane through the points: A(2, 4, 5), B(1, 5, 7) and C(-1, 6, 8)?

A: Let the given points are:

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: Find the equation for the plane through the point Po= (9,2.5) and normal to the vector n= 31 + 10j +…

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Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

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Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

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Q: 8. If the vertices of a triangle are A(8, 5), B(-1, 8) and C(2, -1) where would the centroid (Center…

A: Consider the vertices of a triangle is (x, y). The vertices of a triangle are: A(8, 5), B(-1, 8) and…

Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

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Q: b. Please provide a well explained answer for the follwoing. And explain how to add/subtract…

A: We have to write definition and some basic properties of vectors.

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

A: