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

Q: find the angles between the vectors:x+y=1,2x+y-2z=2

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: Find the angle mesure between the two vectors u and v where : u=-2i + 2j + 4k, v=3i + 8j + 2k write…

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Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Find the area of the parallelogram determined by the vectors u and v.

A: Given any non-zero vectors.

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 the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

Q: Find the area of the parallelogram that has the vectors u and v as adjacent sides, where ||u|| = 2,…

A: The area of the parallelogram is ∥u∥×∥v∥×sinθ=2×12×sinπ3=24×32=123   Here θ= the angle between u and…

Q: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

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Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

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Q: Find the angle between the diagonals of a parallelogram constructed on the vectors a=2 i +j and b=-2…

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Q: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

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Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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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: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (2, 5, 3), Q = (– 3, –…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

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

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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 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 the cross product of the vectors a = 2i + 3j – k, b =i- 2j + 2k.

A: NOTE: Refresh your page if you can't see any equations. . given vectors are

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a…

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Q: Find the median AD of the triangle ABC where positive vectors of the vertices A, B and C are…

A: Vertices of the Triangle ABC given A=i+j,B=4i+6j,C=i-j; Hence, We can take these vectors as the…

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

A: .

Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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Q: Find the angle between the vectors a 0 = and b = 2i+j - 4k. 10i - j - 5k

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Q: Find the angle 0 (in degrees) between the vectors u = -2i - 2j v = -31 + 3j

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Q: The area of the parallelogram whose adjacent sides are the vectors u and v is a) Ju · v| c) Ju x v|…

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Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a –…

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Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

Q: Find the angle between the vectors u = i − 2j + 2k and v = −3i + 6j + 2k.

A: In this question we have to find the angle between the vector.

Q: The angle between the two vectors is not equal to Select one: O True O False u= and v= 0= π

A: Here we use the concept of dot product of the vectors.

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: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (– 6, – 1, 3), Q = (- 1,…

A: The corresponding position vectors with respect to origin are,…

Q: 2. The area of the triangle whose adjacent sides are the vectors u and v is a) Ju · v| c) |u x v|…

A: It is known that, the area of the triangle whose adjacent sides are the vectors A and B is 12A×B.

Q: Find the area of the parallelogram that has the vectors u = (5,-1, 4) and v = (2,-3, 1) as adjacent…

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Q: Determine the angle between the vectors: x 3i + -3j + -7k and y = 12i + 3j +11k

A: x = 3i -3j -7k  y = 12i +3j +11k

Q: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

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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 the parallelogram spanned by the following vectors. u = [4, –6, 5] v = [0, 6, 8]…

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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: 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: Find the dot product of the vectors v = 5i - 3j and w = 2i - j.

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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: answer is following-

Q: Find the angle between the vectors u = - 5i – 3j and v = 6i + 2j + 5k.

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Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

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Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…