Find the volume of the parallelepiped determined by the vectors a = (2, 4, – 1), 6 = (0, 4, 1), č = (2, 4, 1). %3D Volume = cubic-units Add Work Check Answer

Q: Find the dot product of the vectors. v = i + 5j; w = -i + j %3D V. W = Submit Answer

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Q: What is a parallelepiped? What is meant by the parallelepiped determined by the vectors u, v, and w?…

A: A prism, made of parallelograms; a polyhedron with six faces, each of which is a parallelogram.  The…

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

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: Find the dot product of v and u and determine if the vectors are orthogonal. V = The vectors are not…

A: To find dot product of given vector.

Q: Q / Determine the value of b so that vectors 4 = 49-593 V=-2₂0₂-5 w=bs 1, 6 lg are in the Same Plane

A: We have given that the vectors ,  u = 4 , -5 , 3  ,  v = -2 , 0 , -5  ,  w = b , -1 , 6 We know that…

Q: Determine the dot product of vectors a, b when |a| = 5, |b| = 1 and the angle between a and b is…

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Q: (iii) Find the angle between the vectors. a = 8i – j+ 4k, b= 4j+ 2k (iv) Find the volume of the…

A: Given a=8i-j+4k, b=4j+2kTo find angle between two vectors:

Q: If the volume of the parallelepiped determined by the vectors ä, 5, č e R³ is A cubic units, which…

A: Consider the provided question, a→∧3b→∧b→∧c→Let a→∧3b→=u→a→∧3b→∧b→∧c→=u→∧b→∧c→…

Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The area of the parallelogram determined by the vectors u and v is A=u×v. Given u = i + j and v = j.…

Q: (a) Find a nonzero vector orthogonal to the plane through the points P(0,- 2, 0), Q(4, 1, – 2), and…

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Q: Given the points P (1, 2, 2), Q (2, -1, 4), R (3, 5, -2) and S(0,-1,3). (a) Use vectors to calculate…

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

A: Volume of parallelopiped

Q: e) a unit vector perpendicular to both i and i f) the volume of the parallelepiped formed by vectors…

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Q: Consider the regular octagon centered at the origin as shown at right. Eight unit vectors are drawn…

A: By definition, the cross product of two vectors is a vector in the direction perpendicular to the…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 31 + 2j - 3k, b =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the cross product of the vectors ä = and b = .

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Q: Find the volume of the parallelepiped determined by the vectors ?, ?, and ?.   a= i + j,   b= j +…

A: a=  i + j+ 0k b= 0i + j + k c= i + j + k  The required volume is [a b c]=110011111 =1111-0111…

Q: Determine the value(s) of ? such that the vectors [5, ?, −8 ] and [3, ?, ?] are perpendicular.

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Q: Find the volume of the parallelepiped determined by the vectors (0, 4, −5), (2, 0, 5), and (-1,3,0).…

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Q: Find the volume of the parallelepiped determined by the vectors a =i+3j-k, b= 4i+j-2k and c= - =…

A: a=i+3j-k,  b=4i+j-2k  &  c=-2j+5k

Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The vectors u, v, and w. u=i+j-k,v=2i+j+k,w=-i-2j+3k.

Q: Q6. Find the volume of parallelopiped formed by the vectors , and .

A: To find the volume of the parallelepiped formed by given vectors.

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 5, 4), b = (-1,…

A: Given vectors are a=(1,5,4), b=(-1,1,3), c=(5,1,4).

Q: Find the area of the parallelogram with vectors a = 3p+ 2q, b= 2p-qwhere \pl = 4, lq] = 3, (p, q)…

A: To find the area of the parallelogram with the vectors a=3p+2q,b=2p-q where p=4,q=3,p,q=3π4.

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c: a=, b=, c=

A: Given: a=<1,2,3>,b=<-1,1,2>c=<2,1,4>

Q: Find the area of the triangle with two sides given by the vectors a = i – j+ 4k, and b = 2i – 4j+1k

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Q: Find the length of the vectors (a) –2 i + 2j – 4 k: length = (b) 0.47 – 0.4 + 1.6 k: length =

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Q: Given the vectors a=i + j + k,  b= i-j and c=i + 2j + k, determine the volume of tetrahedron

A: Given- Given the vectors a = i + j + k, b = i - j, and c = i + 2j + k.  To find- Determine the…

Q: a. Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and b. find the…

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Q: Find the volume of the parallelepiped determined by the vectors a i+2j-k, b 3i+j-4k and e= -2j+5k. O…

A: The parallelepiped is formed by the vectors, a→= i + 2 j - kb→= 3 i + j - 4 kc→= -2 j + 5 k  volume…

Q: The volume of parallelepiped determined by the vectors u = 2i – k, v = 2j – 3k and .= w = i + j+k is…

A: We use the definition of the volume of a parallelopiped determined by the vectors a, b and c to find…

Q: a. For what vaiue(s) of a are the vectors r= (3, a, 9) and y (a, 12, 18) collinear? b. For what…

A: Collinear and perpendicular vectors

Q: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and (b) find the…

A: The given points are P(1,0,1), Q(-2,1,3), R(4,2,5)  a) Obtain the non zero vector orthogonal to the…

Q: Answer the fellowing muitiple-chorce awestion below algybra A9. w and V are par pandicular vectors…

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Q: V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors…

A: Solution of 1st question.

Q: What is the volume of the parallelepiped determined by the vectors ⟨0,1,4⟩,⟨1,1,1⟩, and ⟨2,0,3⟩?

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Q: If the volume of the parallelepiped determined by the vectors d, b, čeR' is a cubic units, which of…

A: Given, 2a→∧b→∧b→∧c→ Let, 2a→∧b→=u→ Now simplifying the given equation by apply the vector dot…

Q: Find the distance between the two vectors. u= (-6, – 1), v =(1, - 6) O A. 37 О В. 37 О С. 74 O D.…

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Q: Find A:D,AAU ® let Ā = i+2j-K , B=-i+j+ K,itk> D=i+2j-K which vectors are: @ perpendiCular 6…

A: Please see the explanation below

Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

Q: The volume of the parallelepiped determined by the vectors à =,b= and = is: %3D (A) 12 (B) 6 (C) 24…

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Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

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Q: The volume of the parallelepiped determined by the vectors a =,b= and c = is: %3D (A) 12 (B) 6 (C)…

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

Q: Find the signed volume of the slanted box in R" generated by the vectors 27 11 3 vi = 6. V3 = ,V4 =…

A: Given that, v1=0263,v2=-2-1-10,v3=-1-203,v4=-13-20

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

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Q: Find the distance between the two vectors. u = (4, – 8), v = (- 8,8) O A. 100 О В. 4 Ос. 20 O D. 400

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