Prove that the ray AB union ray BA equals the line AB.

Q: 1. Given the points P(5, 3, - 4) and Q(7 - 1, - 3), find the following: a. the vector PO b. PQl

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Q: If two planes intersect, then _____.

A: Intersection of two planes is given by,

Q: Given vectors u and v in the diagram below, shade in all linear combinations cu + dv for (a) -1 1…

A: (a) Shade the linear combination.

Q: 14 Draw each position vector. Then find its magnitude a) [-6, 3, 7] [6,5,-2] X +Z +Y * Y -Z N +Z +X

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i+j and i – 2j as…

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Q: Find the angle between the following pair of lines: i. 7=21-53+k+ 2(31 +23+ 6k) and r = 7î - 6k+ µ(i…

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Q: 1. AB and CD are parallel and 15 centimeters apart, mZBAC = 58° and %3D is the reflection through AB…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem. You can…

Q: 1. Given two vectors, a = nearest degree. [1, 2, 4] and b = [− 6, 0, 3] determine the angle between…

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Q: The diagram shown is a regular hexagon. Please label it as ABCDEF. Write each of the following as a…

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Q: Two vectors 2a − 3b and 3a − b are perpendicular. Find the angle, ?, (correct to the nearest degree)…

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Q: i) ii) Draw a vector diagram for the cyclist's trip. Find the distance covered by the cyclist. (Give…

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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: Find the cross product u x 7 where =5i +4j -2k and 7 = (-1, -7,8). uxv=

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Q: 348, 7.) x and y are vectors between them and 2, respectively, with an angle of 120° of 3x + 27. the…

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Q: Let → a = and → b = . Find k so that → a and → b will be orthogonal (form a 90 degree angle). Let…

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Q: Question 7. Find the angle between the vectors v and w: v = (2,1,3), W = = (12, 6, 18)

A: The given vectors are:.To Find: Angle between the given vectors.

Q: 6- Check if each of the following is orthogonal or not: i- A = ii - A = 1 1 [1 iii - A = 1

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Q: If A(x₁, y₁), B(x, y₂) and C(x3, 13) are the vertices of triangle ABC and x+y=x2 + y2 = x3 + y3,…

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Q: If a line is parallel to the vector 4i + 1j + 4k and passes through the point P = (3, 7,9), then the…

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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: Let v = 2 1 - 3 + 5k, and u = -2 i + 3j - 5k, Calculate vll, ull, Ilv • ūll, and 8 (the angle…

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Q: A. Determine if p=9i-6j-24k and =(-15,10,40) are parallel, orthogonal or neither. B. Determine the…

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Q: ā − Let a = and b = . - Find k so that a and b will be orthogonal (form a 90 degree angle). k=

A: Let .To find  will be orthogonal.

Q: If A (1,2,3) and B (4,6,5), C(8,-5,1) are points in three-dimensions, find. a. AB b. |AC| c. AB AC .

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Q: 8. Given the points A = (1, 2, 4), B = (-1, 1, 3), and C = (-3, -2, 5). Find the equation of the…

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