Every triangle has a balancing point, called the centroid. O True O False

Q: of the corners of a triangle ABC are A (3,-1,0), B (-2, 2, 3) and C (0,0,4). The units are inches.…

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Q: In this figure, the 2 squares are identical in size, the 4 small circles are identical in size, and…

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Q: If a is a vector such that ||a|| = 7, then what is a . a? √7 7 14 49 There's not enough information…

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Q: If a,b,c are vectors such that a.b=a.c,a×a=a×c, then show that b=c

A: Given, a,b,c are vectors such that a·b=a·c, a×a=a×c To prove: b=c

Q: 2. Explain what it means for vectors to be each of the following: a) equal b) opposite c) collinear

A: A) equal vector

Q: Let E, F E R3. Show that E = F if and only if E. A = F·A for all vectors A E R³.

A: Given that E→,F→∈ℝ3. Show that E→=F→if and only if E→·A→=F→·A→for all A→∈ℝ3.

Q: Use the polygon law of addition to draw the resultant vector ( å + b) + ở for the following yectors.

A: The given vectors are added

Q: Let A = (1, 1, -1), B = (-3, 2, -2), and C = (2, 2, -4). Prove that ABC is a right-angled triangle.…

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Q: u = and v = 1 -1,

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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: ) Let 1 3 2 -2 1 -2 2 8 6. be given vectors in R³. Determine if b is a linear combination of v1, v2…

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Q: Determine it the set belon defines a vector Supspace . Justif the conclusio - All vectors <x, in R3…

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Q: In the given diagram, which is the equivalent of vector

A: sum of vectors of closed triangle is 0 if we choose one direction -- Here if choose anticlockwise…

Q: 1. The vertices of a triangle are located at A(4,1, –3), B(-2,5,4) and C(0, 1, 6). Using vector…

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Q: Let v1, . . . , vp be vectors in R n . Show that if vp ∈ span{v1, . . . , vp−1}, then span{v1, . . .…

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Q: 37 Suppose that AB, AC, and AD are directed line segments of u, v, and u + v, respectively, with…

A: Question 37:Part 2: Explanation:Step 1: Let's denote the vectors AB, AC, and AD as \(\vec{u}\),…

Q: Let v = (a, b, c). Calculate v × i, v × j, and v × k.

A: given: v=a,b,c we have to calculate v×i, v×j and v×k

Q: If A is diagonalizable, then A is similar to D. Select one: O True O False

A: Given   if matrix a is diagonalizable then A is SIMILAR  to D

Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

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Q: Investigate whether the following vector set is base or not! a. D= {(2,0,-3), (1, 1, 2)}

A: We know, a vector set D is called basis of the vector space V if , I) D is Linearly independent II)…

Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

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Q: Let O be any point in space. a, b, c are the vectors from O to the three vertices of parallelogram…

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Q: A free vector is Select one: O a. a directed line. O b. a directed line-segment in 3- space. c.…

A: A vector whose point of application is not fixed but magnitude and direction is, is called free…

Q: 7. Write the vector w in terms of u and v, given that the terminal point of w bisects the line…

A: This question is related to vectors, we will solve it using given information.

Q: Let V = (a, b, c, d), such that a = 2b − c, b = 2d − 3c, and d = a − b + c. Find the dimension of V…

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Q: This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry.…

A: (a) Here, u=v=u+v=1. ⇒u2=v2=u+v2=u+v·u+v ⇒(u+v)·u+v=1⇒u·u+2u·v+v·v=1⇒u2+2uvcos(θ)+v2=1⇒1+2…

Q: X Let W be the union of the first and third quadrants in the xy-plane. That is, let W = () and b…

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Q: The heigh of a sqare pyramid is 21 cm, the length of the sides of the square is 40 cm. What are the…

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