29. Find the volume of the parallelepiped PQRS if the vectors V(PQ). V(PR), and V(PS) are, respectively, i + 3j + 2k. 2i +j-k, andi- 2j + k.

Q: Find the volume of the parallelepiped with sides give by the three vectors a = 2i – 2j+ 3k, b = 5i+…

A: a→ = 2i^ -2j^ +3k^b→ = 5i^ +2j^ +6k^c→ =-3i^ +2j^ -2k^Volume of parallellpiped = a.(bx c¯

Q: The scalar triple product of three vectors gives the volume of the three-dimensional parallelepiped…

A: The Volume of the three - dimensional parallelepiped descrived by the vectors  is the scalar tripple…

Q: = 2. Are the vectors V = (2, — 4, 1) and w Show work and briefly explain. (3, 2, 2) orthogonal? 3.…

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Q: Q4) The vector product of two vectors is scalar product. F O T

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Q: Find a vector v parallel to the intersection of the planes - (x + y + 3z) = 4 and 3y - 3x - z = 7.…

A: Step 1: Step 2: Step 3: Step 4:

Q: Consider the three vectors u = (0, -2,3), v = (1,-4,0) and w=(-4,3,-5). a) Find the cross product…

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Q: 8. If you know that the vectors a = 4i-j + 2k and b =4i-2j-5k, then the lengthvector %3D a - 2b = A.…

A: To find: The length of the vector a→-2b→. Given: The vectors are a→=4i-j+2k and b→=4i-2j-5k. Concept…

Q: What is the area of the parallelogram formed by the vectors v = (1,0, 1) and w = (0, 2, 2) tail to…

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Q: ● Let u = 2-25 - 2k + ● and = 2î - 2Ĵ+k. Find a vector w such that the parallelepiped spanned by u,…

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Q: 4. Consider the vectors u,v and w are defined, u = 3i-j+4k, v = 4i – 2j +6k and w= 5i+2k (a) Express…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: We have the following vectors: A = 2i - 2j + 3k, B=- -2i + 6j - 2k, C= -4i - 2j + k. Determine: a)…

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Q: Find the volume of the parallelepiped defined by the vectors 2 -4 2 -5 -3 Volume =

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: Consider the parallelepiped P in R³ determined by the vectors u= [2 -1 -1], v= [3 -1 -2] and w=[-2 2…

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Q: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…

Q: A = x6- y9+z3 B = x6- y3+z9 C = x 2- yl-zl For the given vectors A,B, and C show that whether C is…

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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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