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 right triangle, Find the area of the triangle.

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

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Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

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Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

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Q: B- For what values of a1 are the vectors [a1,4,3] and [3,-2,12] are 1) Orthogonal? 2) Parallel? 3)…

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A: given

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: For what values of c are the vectors [-8, c, 4] and [c, c²,c] orthogonal?

A: For orthogonal,dot product of vectors is equal to zero.

Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

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Q: Find the Euclidean distance between the given vectors. -- - - -8 -26 d(m, n) = Ex: 1

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

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Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

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Q: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

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Q: One of the following vectors lies in span{ 2+x + æ2, 3+-2a2} (A) 5 + 3x + 4x2 (B) 5 + 3x + 5æ? (C) 5…

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Q: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

Q: Given that the vectors a=(6,-1,2k)  and b=(-1,k+1,4) are perpendicular, what is the value of k?

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Q: 7. Find the values of m that will make the following vectors perpendicular. à = (2m, 3,1), b = (m,…

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Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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Q: 2. If å and b are two vectors with lengths 2 and 5 and angles between 150°, respectively, obtain the…

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Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

A: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

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

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Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

Q: Given the vectors a=(1,2,3) and b=(1,−1,2), what is the dot product a⋅b⋅a?

A: Solution :- let a = (x1, y1, z1) and    b = (x2, y2, z2)  be any two vectors then their dot product…

Q: Given two vectors a = (−2, 1, 3) and b = (3, −1, 2), does c = (−18, 7, 1) lie on the plane…

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Q: given the vectors from R, (-5 0 3) belongs to span{v,, V2, V3}. Select one: O True O False

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Q: For what values of ai are the vectors [a1,4,3] and [3,-2,12] are a) orthogonal? b) Parallel? c) Have…

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Q: ) Below is a diagram of the dotted cube with edges of length 5. Suppose (5, 0,0), v = (0, 5, 0), and…

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Q: A- If P1(1,3, –2) and P2(4,7,-2) are two points. 1- Compute the length of 2P,P2 2- Is the vector…

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Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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

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Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

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Q: If the vectors in the figure satisfy Ju| = |v| = 1 and u + v + w = 0, what is |w|? u |w| =

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