Find the volume of the parallelepiped determined by the vectors å = (3, 4, – 1), 6 = (0, 2, 1), c = (2, 5, 1). Volume = cubic-units

Q: Use the cross product and determine the volume of the parallelepiped generated by the three vectors…

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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find 1 the area of the parallelogram determined by u…

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Q: Find the angle 0 between the vectors. u = (2, 2), v = (4, -4)

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 1, 2, 2   b = −1,…

A: This question is related to vectors and volume of parallelepiped,  we will solve it using given…

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: Find a vector ū that is parallel to the yz-plane and perpendicular to the vector i = (0, 2, 2).

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Q: compute the volume of the parallelepiped defind by the vectors v1(1,3,1) v2(2,1,-1) v3(1,0,1)

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Q: Find the volume of the parallelepiped determined by the vectors a = (3, 4, – 1), b = (0, 4, 2), с 3…

A: Given the vectors, a→=3,4,-1b→=0,4,2c→=2,5,1

Q: Find the cross products u x v and v xu for the vectors u = (4,4,0) and v = (0,2, - 5).

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Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: = Find the volume of the parallelepiped determined by the vectors a c = (2, 3, 1). Volume =…

A: The volume is given by scalar triple product of vectors. a→=4,2,-1, b→=0,3,2,c→=2,3,1

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2). b= (0,…

A: The volume Parallelepiped by the vector a, b and c is given as:

Q: Find the volume of the parallelepiped determined by the vectors a č = (2, 4, 1). (3, 5, – 1), 6 =…

A: The volume, V , of a parallelepiped is calculated using the scalar triple product, V=c·(a×b) . Use…

Q: 5- Find the volume of the box (parallelepiped) determined by the vectors 0 = (0,0,0), B = (1,1,2)…

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Q: The unit vectors normal to the vectors (2, - 8,11) and (- 3,0,5) are

A: Find unit vector

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: Find the angle θ between the two vectors.u = (0, 4, 0, −1), v = (1, 1, 3, −3)

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 1, 2, 4   b = −1,…

A: First find cross product of b and c and take dot product with a

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: 5. Calculate the area of the parallelogram formed by the vectors (4, 10, 9) and (3, 1, -2).

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Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (4, 2, -2), b = 3…

A: Given:- a = (4, 2,-2), b = (0, 2, 1), c = (4, -3, 4) To find :- Volume of Parallelepiped

Q: nd the angle (to the nearest tenth of a degree) between the vectors  u = and v=

A: Angle between vectors u and v is θ = arc cosu.vuv

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = ‹6, 2, -1›,     b…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: We will use the given formula of volume to find the volume of the tetrahedron.

Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

Q: Find the volurne of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2), b =…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Find the volume of the parallelepiped determined by the following vectors. a) u = (3,2,8), v = (5,…

A: Find your answer below

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (2, −1, 0), v = (−1,…

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Q: Find the angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

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Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

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

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1.3,4). b =…

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Q: Find the area of a parallelogram with two sides identified by vectors from the origin to the points…

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Q: u

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Q: Find volume of the parallelepiped determined by the vectors a = (8, 1,0), E b = : (1,4, 1), and c =…

A: The given vectors are a=8,1,0, b=1,4,1 and c=1,1,10

Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: Find the volume of the parallelepiped determined by vectors , and

A: Find the volume of the parallelepiped determined by vectors <3,1,4>, <2,0,2> and…

Q: 9. Use the cross product and determine the volume of the parallelepiped generated by the three…

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Q: 6-Determine the volume of the parallelepiped formed by the vectors U= [2,1,3], v= [1, -4,2] and w=[…

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.