Given a = [1,3,-2] and b = [-2, 5, 1]. %3D Determine: a)The magnitude of the sum of the given vectors b)The orthogonal vector to the given vectors c) The area of the parallelogram bound by the given vectors

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 area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

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 value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b,…

A: Given that P , Q & R lie on a straight line. It means vectors are coplanar . since if vectors…

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: It is known that the area of the parallelogram P formed by the vectors u and V is 14 square units…

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Q: Consider the parallelogram given by vectors [12, 5], and [18, 0]. Give the lengths of the altitudes…

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Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: given two vectors v m which are perpendicular. under which condition is V+W perpendicular to V-W?

A: Since vectors v and w are perpendicular so, their dot product is 0

Q: Find the resultant using (a) the parallelogram method, and (b) by summing up components. For the…

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

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Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

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: If a = 2i -j+2k and b =i+2j-2k, find two vectors c and d satisfying all the following conditions:…

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Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

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

A:

Q: Find the area of the parallelogram that has the vectors as adjacent sides. u- (3, -5, 3) v = (2, 0,…

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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: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: If the points with position vectors 10i+3j.12i-5j and ai+11j are collinear, Find the value of a.

A: The position vectors of the points which are collinear is: 10i+3j ,     12i-5j ,      ai+11j

Q: Suppose u = (0, –2) and v = (2, 2) are two vectors that form the sides of a parallelogram. Then the…

A: This question is based on parallelogram diagonal.

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

A: .

Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

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

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Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az * O…

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Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

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: Given the vectors a=(1,2,3) and b=(1,−1,2), what is the dot product a⋅b⋅a?

A: Solution :- let a = (x1, y1, z1) and    b = (x2, y2, z2)  be any two vectors then their dot product…

Q: Given column vectors a and b, find the SVD of: (a) A = abT. (b) B = ab" + ba" when aTb= 0.

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

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

A: Area of the prallelogram using cross product

Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

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

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

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Q: The sum of two vectors is called the ___________, and it can be represented geo-metrically as the…

A: The sum of two vectors is called the resultant, and it can be represented geometrically as the…

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: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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

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Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: Show that LM = 2AB.

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Q: value

A: If, P, Q & R are collinear, then,  The position vector of QP is, The position vector of P - the…

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.