D1.4. The three vertices of a triangle are located at A(6, -1, 2), B(-2,3, -4), and C(-3, 1, 5). Find: (a) RAB X RAC: (b) the area of the triangle; (c) a unit vector perpendicular to the plane in which the triangle is located.

Q: In the picture below, x = (*) and (3). V= 7 u = The vectors p and r are also shown in the picture,…

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Q: The magnitude of three vectors a, b, and c form a right triangle. Given the equation, what is the…

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Q: If A = 4a, - 6a, + a, and B = 2a, + 5a,, find: (a) A B +2|B (b) a unit vector perpendicular to both…

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Q: For the given vectors: å = (-2,-3), 5 = (1,–2), 7 = (0,3), find: (a) 2å – 35 + ở (b) angle between…

A: Given the vectors a,b and c. The solution to the given questions are as follows.

Q: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: 39. Given a = (3, -4) and b = (1, 2). Find the vector 2 a. (3,4) a. b. 2,4) c. (6,-8) d. (5,-2)

A: From the given statement,

Q: Three vectors are given: A =il+j2+23,B= &4-§2+23, and C= -x4. Calculate: (a) A+B+C. (b) A+B-2C. (c)…

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Q: Determine whether the lines h and I, intersect, are parallel, or are skew. 1: n= 4i+3j+ (i-j+6k) 12:…

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Q: Find the angle between lines AB and AC where the point A(4,4,1), the point B(−4,7,7), and the point…

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Q: Q1: suppose the middle of each side of the triangle is a vector from the vertex (1,2,3), (3,2,1),…

A: Vectors

Q: Find the direction cosines of v =〈3, 6, −2〉.

A: Given vector is v=3,6,-2. To find the direction cosines of given vector. Solution: We know that if…

Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

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Q: Find the cosine of the angle between the planes -3x - 4y – 3z = 3 and the plane - 1x - 3y + 3z = -2.

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Q: 02. Given the vectors : A = (3.-1, 2), B = (0, 1, 1) and C- (2, 2,-1), find: the angles between the…

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Q: Find the cross product of the vectors a=⟨2,3,−2⟩ and b=⟨−3,−6,−4⟩. Select one: a. ⟨0,2,−3⟩ b.…

A: a*b = <-24,14,-3> option 'e' is correct

Q: 16. Let u=2i+2j and v=-i+√3j. Find the angle between these vectors. (Hint: Graph each.) A. 120…

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Q: 13. Prove that the three points (-3, 2, 4), (6, 1, 2), and (-12, 3, 6) are collinear by using the…

A: To solve the following problem

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

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Q: Rossie is a simple robot in the plane, with Start position at the origin O, facing the positive…

A: We consider the unit of  to be degrees, unless specified otherwise. a) All  such that  bring Rosie…

Q: Q5) Given points A (10, -3, 4) and B(-4, 3, 5), find: a. The distance from A to B. b. A unit vector…

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Q: Find the direction of v:v =(7,-2)

A: Given: v→=7,-2