Q2) The vector of length (15) and in direction of Ã=i-2j-k is: * 1 :k 15(i– 2j-k) i+ خیار 3 15 30 i+ 15 15i - 30ј — 15k 2 ja O 1

Q: The vector from the origin to point A is given as (-2, 3, 5) and the unit vector directed from the…

A: A = (-2, 3, 5)  Thus, position vector of A,  a =  -2ax + 3ay + 5az   UB  =  0.535ax + 0.802ay -…

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Find two vectors v, and 02 whose sum is (-5, 5, –3), where 0 is parallel to (-1, –2, 1) while Dz is…

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Q: نقطتان )2( The cross product of the vectors 3ax + 4ay - 5az and -ax + ay - * ,2az is -Зах -11ау -7az…

A: Dot product

Q: If a vector gets multiplied by a positive number, its direction will be *.reversed FO TO

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Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: Find a vector that has the same direction as 8i-j+4K but has a length of 6

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Q: Choose a vector (b1, b2, b3) for which Ax = b can be solved, and another vector b that allows no…

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Q: Suppose that uj and u2 are orthogonal vectors, with u1 = 2 and u2|| = 4. Find |5u1 - u2 ||. ||5u1 -…

A: We have to solve given problem: Let  U1=(a1,a2)  U2=(b1,b2)5U1-U2=5(a1,a2)-(b1,b2)…

Q: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: Determine the resulting vector when á = (-2,4) is rotated 60° clockwise and increased in size %3D by…

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Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

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Q: For the vectors u = (-1,4) and v = (-2,2), calculate proj, u and scal,u. projyu =

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Q: What is the area of the parallelogram determined by the vectors v = (1, 3, 6) and w = (-1,0, 3)?

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Q: 2. If a --i+3j-k and E-2itj-3K decompose vectoes E into the sum of two vectors, one is paralled and…

A: This question can be solved using the concept of condition of two vectors to be parallel and…

Q: Determine which of the vectors is parallel to z and which is orthogonal to z if z = (3, 2) Show work…

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Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

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

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Q: 1. Express A = (3, 1, –1) as B+ C, where B is parallel to the vector (1, 4, 2) and C is…

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Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

A: Follow next step

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: Which vector below is NOT orthogonal to i = -2î – 8ŷ + 7k ? -- 1 2 8. O 0 î + 0ĵ + 0k 3. 1 O 4 î - )…

A: Given problem:-

Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Suppose (vector u)=(3,-4,-5) and Vector v=(2,-1,2)u+v=?u-v=?v-u=?3u=?(-1/4)v=?2u-3v=?I appreciate…

A: u=(3,-4,-5)v=(2,-1,2)

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

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: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

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: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is

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Q: 1. The vector in the opposite direction to u = (-1,0) and of half its length is 2. The vector of…

A: 1.The vector is u=<-1,0>2.The vector is v=<-4,5,-3>

Q: Suppose the vector ū =<3,1,-47 is translated so that it's heach is at the point C-1,2,3). where ito…

A: Given that the vector u→ = 3,1,-4 is translated such that its head is at the point (-1,2,3). We have…

Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

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Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: Find two vectors v1 and vz whose sum is (-4, –4, 5), where vj is parallel to (1, 1, –2) while v2 is…

A: we have to find the two vectors v1→ and v2→ whose sum is -4,-4,5 where v1→ is parallel to 1,1,-2…

Q: Find two vectors ūj and īz whose sum is (-5, –3), where vj is parallel to (2, 5) while īz is…

A: To find - Find two vectors v1¯ and v2¯ whose sum is -5, -3, where v1¯ is parallel to 2, 5 while v2¯…

Q: For the vectors u = (-4,1) and v = (-2,3), calculate projyu and scal, u. projyu = OD

A: Here I am attaching image so that you understand each and every step.

Q: 1. The vector in the opposite direction to u = (-2, 2) and of half its length is 2. The vector of…

A: Given vector is u→=-2i+2j To find the vector in opposite direction and half its length.

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: Find two vectors a and b such that projba = &lt;4, -2, 8&gt;. That's all the information I was…

A: It is given that,

Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

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