Let ABC be a triangle and let a line / intersect the AB, BC, AC at C,A,B respectively. Let P be the corresponding Miquel point. Prove that the orthogonal projections of P on the lines AB, AC, BC and l are collinear.

Q: two vectors u = [5,4, -3], v = [1, -2, -1] form an angle θ that can be less than 90 ° (acute),…

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Q: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

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Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: Consider the vector v between (−3,3,−4) and (−2,−4,8) a) the vector v is ? b) the length of v is ?…

A: (a) The vector v is between the vectors -3,3,-4 and -2,-4,8. Subtract the vector -2,-4,8 from…

Q: Consider the three points A = (-2,2,-2), B = (-3,5,5) and C = (1, -2,-2). Determine the vectors u =…

A: Since your question has more than three subparts, so as per Bartleby Guidelines we are answering…

Q: a) If Jä| = 2, JB| = 3 and the angle between å and b is, find the length of å- 2b. %3D %3D

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Q: Given the points P(8,4, 3), P2(1,8,0) and P3(10,0.4). a) Find the distance from P, to P2. b) Find…

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Q: . Using the cross product, a-) Check if the following 4 points are the consecutive vertices of a…

A: a)…

Q: Let  u = -5i + 3j + 3k, v = -4i + 3k and w = 3i - 4j + 3k. a) Find | -4u + v + j |.  b)Find the…

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Q: 7. Given three point A(1, 1, 3), B(-14, 4, 21) and C(-4, 2, 9), a) use a vector method to show that…

A: We have to solve given Questions.

Q: In a regular hexagon ABCDEF point G is the midpoint of line segment EF, point S is the intersection…

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Q: Suppose that OABC is a parallelogram. Let M be the midpoint of OA and let P be the point of…

A: 1st we will draw diagram of the given situation and then find position of P using section formula…

Q: Three points with position vectors a, b, and c will be collinear (lie on a line) if the…

A: Given that:         Position vectors of points areA(2,2,3), B(6,1,5) and C(-2,4,3)

Q: If the position vectors of the points A, B, C, D are a = i +j+k, b = 2i+ 3j, c = 3i+ 5j – 2k, d= k –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

Q: Suppose we have the triangle with vertices P(1,6, 1), Q(-3,7,–3), and R(5, 1, 1). Answer the…

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Q: 4. The diagram is a rectangular prism. Let u AB, = AD and w = AE. Express each vector as a linear…

A: The diagram is a rectangular prism. Let .To express each of the following vectors as a linear…

Q: Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by…

A: A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A,…

Q: 4. ABP is a triangle, M is a point on AP. AB = a, AM = 26, and MP = b. N is the midpoint of BP. C is…

A: Follow the steps.

Q: 1. For two vectors: B=6â, +2â, -4â, A=4â, -10â, +5â a) Find the angle between these vectors. b)…

A: Given two vector  We have to find the angle between the two vectors.

Q: A parallelogram is formed by the vectors = [3,0,-1] and A) 2-√√35 B) 12 sq.un. C) 5/10 sq.un. D)…

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Q: 1. Given vector PQ with P(2,-3) and Q(-1,5), find the following. a) Component form of PQ b) PO c)…

A: 1.  (a) Given vector P=2,-3  and  Q=-1,5 . Therefore, Component for of PQ→ will always passes…

Q: The positions of two villages P and Q from a town O are represented by vectors OP and OQ where OP-p…

A: The given diagram is shown below:a.) It is required to express QP​ in terms of p and q. Create a…