The three vertices of at riangle are located at A(6,−1,2), B(−2,3,−4), and C(−3,1,5). Find: (a) AB ×AC;( b) the area of the triangle; (c)a unit vector perpendicular to the plane in which the triangle is located.

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A: ANSWER IS GIVEN BELOW.

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A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

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A: Topic:- vector

Q: The volume of the parallelepiped determined by the vectors a =,b = and c = is: (A) 12 (B) 6 (C) 24…

A: The given vectors are a→=3,4,5, b→=2,1,-1 and c→=3,2,1

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Q: The volume of the parallelepiped determined by the vectors à =,b = and c= is: (A) 12 (B) 6 (C) 24…

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Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

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Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

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A: n=-3i-4j+4k  and P(2,-7,5)

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A: To find the equation of line intersection of given planes.

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A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

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A: Cross product of the vectors

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Q: b) Find the center and radius of the sphere x+y+z6x+4y-10z+25%=D0. C) Compute a ·b, axb, and…

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Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = j, v = j + k

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = i − j + k, v = i + k

A: Given vectorsu = i-j+k , v = i+kArea of parallelogram is equal to u x v

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Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

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A: This question is related to volume of parallelepiped, we will solve it by using the formula of…

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Q: Find the angle a between the vectors L3] and]

A: Find the angle between vector s

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^