If OABC is a tetrahedron where O is the origin and A, B and C are the other three vertices with positio →→ ->> vectors a, b and c, respectively, then prove that the centre of the sphere circumscribing the tetrahedro ở xã tớ xả tả cả xơ) →→→>> is given by position vector

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: 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: 1. Letz =1+i,1,=-1+i, locate the numbers z+ z, and , vectorially in the rectangular coordinate…

A: We are Given that : z1=1+iz2=-1+i ⇒z1+z2=(1+i)+(-1+i)=2i and  ⇒z1-z2=(1+i)-(-1+i)=1+i+1-i=2

Q: If a, b and care non-coplanar vectors, prove that the four points 2a+3b-c, a-2b+3c -> 3g+4b-2c and…

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Q: Is a triange with the verticies A(7,1) B(0,4) and C(-4,-8) a right triangle yes or no?

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Q: Prove that the points with position vectors a+2b, 2a−b and 3a−4b are collinear.

A: We have to use determinant method to solve.

Q: Prove that three points P(5,-4), Q(-3,8) and R(1,2) on the rectangular coordinate plane are…

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Q: 6) Consider the three points in the plane given by their coordinates: A = (0,0) B=(2,2) C=(3,5).…

A: I have explained everything with in the solution. Please go through that

Q: 10.43. For nonempty sets A, B and C, let ƒ : A → B and g : B → C be functions. a. Prove: If go f is…

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Q: Prove if AABC has complementary triangle AA'B'C' and centroid G, then the six triangles AGA'C,…

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Q: a) Draw the vector 2 - 3 + W. b) Show how to use the parallelogram rule to add u and w

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Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: Given a triangle with vertices: (-3,-3),  (2,3),  (5,-2) Find the exact location of the centroid.

A: Note:-Since you asked multiple questions according to our policy we can answer only first the…

Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…