Define scalar product of two vectors . Show of two vectors . Show that scalar product of vectors satisfies the commutative and distributive laws.

Q: The covariant and contravariant components of vectors can be transformed one to other using metric…

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Q: a,b,c are all vectors. For the vectors:  a = 3i+4k ; b = 2i-j ; c =i+j-5k calculate: 1) vector c •…

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Q: Given the following vectors ā = -1,–2),5 = (-3,-4),c = 2,-1),đ = (-4,3) %3D Use the dot product and…

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Q: A. IF V = yi - x), find curt(V) and V.V B. Find the value of the constant B such that the vectors: u…

A: We can find the curl and divergence of vectors by using the formula The condition for the vectors to…

Q: The sides of a rectangle are formed by vectors A and B with |A| =2 and |B| = 5. Determine the area…

A: topic - vectors

Q: Express the vector 7i - 6j + 6k as a product of its length and direction. 7i - 6j + 6k =[Oi+…

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Q: Calculate the cross products of the unit vectors i × k and k ×j. (Give your answers using component…

A: We have to write value of cross product of I x k and k x j

Q: Find the area of the parallelogram that had the given vectors as adjacent sides. Use a computer…

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Q: Using vectors, prove that if the diagonals of a rectangle are perpendicular, then the rectangle is a…

A: To Prove- Using vectors, prove that if the diagonals of a rectangle are perpendicular, then the…

Q: Find the length of the vectors. (i) 5i - 5j - 3k (ii) 1.4i + 0.6j + 2.8k

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Q: represent a scalar, a vector, or ne the expression in its proper categ ü, ö, and w are vectors, and…

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

Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

A: For a given vector v→, length of the vector is denoted by v→  and direction vector is obtained by…

Q: Graph and find the product. Then find the magnitude of both the original vector and the scalar…

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Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

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Q: 4 Are the vectors and 2 linearly independent? Choose If they are linearly dependent, find scalars…

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Q: With the given the three vectors A, B, C. Determine the dot product of vector A and C A= 2i - 3j +…

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Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k = 11 6.…

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Q: Diven two vectors A= (2i - 3j + 7k) and B = (si + j + 2k) find: a)A+B: (b) A-B () A-B: (d) AxB.

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Q: 4. Show that a 6 a + %3D

A: Here simply open the squre term and then simplify as a.b=b.a

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u= (-…

A: The given vectors are                  u=-12, 0, 6 and v=1, 3,4 To compute the dot product of the…

Q: Given the pair of vectors, A = (8.00î – 2.00j) and B = (-2.00î + 8.00j), use the definition of a…

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Q: Write down an expression for a unit vector parallel to the resultant of two vectors u and v (in…

A: To solve this question we will use the concept of resultant of vectors and unit vector parallel to a…

Q: Given the attached picture determine whether the cross product of vectors w and v is directed into…

A: We must know that cross product of any two vectors will result in a vector that has the direction…

Q: Show all work to calculate the value of x that makes the two vectors orthogonal to each other. v- 6i…

A: →Orthogonal vectors: Two vectors are said to be orthogonal, if angle between both vector is 90°. →To…

Q: (1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle…

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Q: Given two vectors A = 2i + 3j- 2k B = 3i- 4j- 6k Determine the vector that defines the direction of…

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Q: If vector a= and vector b=, find a · b (the dot product of vector a and vector b).

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Q: Determine the scalars K and S that make the vector u a linear combination of the vectors v and w.…

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Q: Show that the vectors are parallel, and determine whether they have the same direction or opposite…

A: Given: a=<a1, a2>=<6, 18>b=<b1, b2>=<-4, -12>

Q: Select all statements which are TRUE. For statements with cross products, assume the vectors are in…

A: Let's find.

Q: a. ā· (5 × ¤) b. ä x (5· č) c. âx (5 x č) с.

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Q: Let ā =, b=,č =. a. What is a +b b. What is a ·6 c. What is a x č d. Are the vectors a and b…

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Q: To enter vectors use the less than symbols from the keyboard and separate the components with a…

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Q: Consider vectors a and b. a = 2i + j, b = i + 3j (a) Determine the vector sum a + b and express it…

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Q: Find a unit vector orthogonal to the vectors 5i + 8j + 3k and 4i + 8j + 8k with non-negative first…

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Q: If two vectors a+b and a-b are parallel, then a and b are parallel. Select one: O True O False

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Q: ZA B side of cube = 10 cm 1. write vector notation in Cartesian coordinates 2. what is the length of…

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Q: What are tensors? Give examples and answer the following * Write four forms of dot product for two…

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Q: -22 -18 and = 2 Find out the area of the triangle whose two sides are given by the vectors: v = 8…

A: Area =12v1×v2

Q: Determine a unit vector perpendicular to the plane of à = 2î – 6j – 3k and B = 4î + 3j – k| (b) Find…

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Q: 2) Let A, B and C coordinates. Find: a) The calculate a mixed product of vectors (5a, -b, 3c). b)…

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Q: Let a. b, and c be three-dimensional vectors. Identify whether the expression a- (b x c) will result…

A: We can solve this as follows:

Q: If ö1 = - 9i- 2j and v2 = - 4i +93, then find - 971 + 302. %3D Type your answer as a linear…

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Q: a) Express vectors G = psinpa,- pcospa, + pa̟ in rectangular coordinates. %3D

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