What is the cCToss product of the vectors 2i + 3j + k and 6i + 9j + 3k? Explain why your answer is correct.

Q: How do you find the dot product a. bof two vectors if you know their lengths and the angle between…

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Q: Express EC by combinations of the vectors a, b and 7.

A: We have to write EC vector in terms of a,b and c

Q: Find the vector in AB R2 given in the figure. 6 AB = help 4 (vectors) 1 2 3 -1 -6 -5 -4 -3 -2 -1 6.…

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Q: Find the angle between two vectors: A=31+4j-5k, (1) Scalar product. (2) vector product. B = 3i+4j+5k…

A: To find the angle between two vectors: A→=3i^+4j^-5k^, B→=3i^+4j^+5k^ by using: 1 Scalar product2…

Q: Find the dot product of the pair of vectors (-2, 5) and (4, 1).

A: Given : < -2 , 5 > and < 4 , 1 >

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: What is the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

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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: What is the cross product of the vectorS 2i + 3j + k and 61 + 9j + 3k? Explain why your answer is…

A: Cross Product: Cross product of two vectors is the method of multiplication of two vectors. A cross…

Q: How do you know if 3 vectors span R^3? Is there any example?

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Q: Show that the vectors are orthogonal.

A: Let the given vectors be v=0i+-4j,u=-7i+0j.

Q: Find the sum of the given vectors. a - (3, 0, 2), b- (0, 6, 0) Illustrate geometrically.

A: Given, Two vectors  a = ⟨3, 0, 2⟩   b = ⟨0, 6, 0⟩  We have to find the sum of vectors and illustrate…

Q: What is the staring point of the vector i = -3i + 2j, if the ending point is (-2, 1)?

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Q: 1. Explain how two vectors are summed (added). How must the vectors be physically arranged? b…

A: Let two vectors and define addition and substraction

Q: How do you find the cross product a x b of two vectors if you know their lengths and the angle…

A: If you know the length of the two vectors a and b then, you essentially know |a| and |b| And then…

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 the parallelogram whose diagonals are represented by the vectors a =(3,-3,1) and b…

A: See this solution in below

Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: What is the magnitude of the cross product of two parallel vectors? The magnitude of the cross…

A: We have to find projection

Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: find the cosine of the angle between the vectors. (1, 1, 1), (2, −1, 2)

A: Given: (1, 1, 1), (2, −1, 2)

Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

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Q: Although I expected vector operations to produce another vector, the dot product of two vectors is…

A: The dot product of vectors is also known as scalar product of vectors. When we find dot product of…

Q: What is the magnitude of the cross product of two parallel vectors? The magnitude of the cross…

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Q: can you add 3 vectors using the parallelogram method? support you answer

A: Parallelogram law : if two vector quantity are represented by the two adjacent side of a…

Q: What is the dot product of the vectors a = 4i + 3j and b = -3i + 4j?

A: Solution is given below:

Q: The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j…

A: Use Cross product of vector

Q: How can you tell when vectors span a certain R^? Please explain in the most simplistic detail>

A: Let S=v1,v2,v3 And v1=1-12;v2=213;v3=-102 Does SpanS=ℝ3? if any vector in ℝ3 can be expressed or…

Q: Determine the dot product of the two vectors shown in the diagram. (3.5) 1. -5 4 -2 -11 23 4 5 -2+…

A: Dot product of the given vectors

Q: Express the vectors in terms of their lengths anddirections. 2i - 3j + 6k

A: The given vector is a=2i-3j+6k. Compute the length of the vector as follows. a=22+-32+62=4+9+36=49=7…

Q: Find the dot product of u = u=(-4,-9) and v=(3,-2)

A: Given: u=(-4,-9)v=(3,-2)

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: What is the size of the angle between the vectors a = (2, 5, -1) and b = (-3, 2, 6)?

A: Given  a = (2, 5, -1) and b = (-3, 2, 6) To find angle between two vectors:

Q: Express the vector -8i-4j-8k as a product of its length and direction.

A: Given vector v→=-8i-4j-8k

Q: Given the vector A 2i +3 j, what is 3 A? Expand vector and collect like terms (simplify).

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

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Q: Find the area of the parallelogram whose diagonals are represented by the vectors a = (3,-3,1) and b…

A: As we know that; The expression for the area of the parallelogram with the diagonals a→ and b→.…

Q: What is the dot product of the vectors (4, −10, 3) and (1, 1, 5)? a) -113 b) 0 c) 4 or d) 9

A: Given :(4, −10, 3) and (1, 1, 5)

Q: Illustrate and explain how to compute the vector product of two vectors.

A: Given query is to find explain vector product.

Q: what Is the v product of two vectors a=C1,4)-2),

A: Which is a scalar quantity.

Q: Find the area of the parallelogram defined by the vectors (9,1) , (-5,5)

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Q: Determine the dot product of the vectors а 3 (-3,—2, 3), b %3D (2,1,-2). b = (2,1,–2). a = 1. а:b —…

A: Solve for dot product

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

A:

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.